Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
87101	Find the Absolute Max and Min over the Interval	(4x)/(x^2+1)	$\frac{4 x}{x^{2} + 1}$ $\frac{4 x}{x^{2} + 1}$
87102	Find the Absolute Max and Min over the Interval	f(x)=sin(x)+cos(x) , [0,2pi]	$f (x) = sin (x) + cos (x)$ $f (x) = \sin (x) + \cos (x)$ , $[0, 2 π]$ $[0, 2 π]$
87103	Find the Absolute Max and Min over the Interval	f(x)=12x^(2/3)+8 , [-8,1]	$f (x) = 12 x^{\frac{2}{3}} + 8$ $f (x) = 12 x^{\frac{2}{3}} + 8$ , $[- 8, 1]$ $[- 8, 1]$
87104	Find the Absolute Max and Min over the Interval	f(x)=x/(x^2+9) on -5 , 5	$f (x) = \frac{x}{x^{2} + 9}$ $f (x) = \frac{x}{x^{2} + 9}$ on $- 5$ $- 5$ , $5$ $5$
87105	Find the Absolute Max and Min over the Interval	f(x)=x^3-5x-5 ; between 1 and 4	$f (x) = x^{3} - 5 x - 5$ $f (x) = x^{3} - 5 x - 5$ ; between $1$ $1$ and $4$ $4$
87106	Find the Absolute Max and Min over the Interval	p=1/12x^2-14x+588 , 0<=x<=84	$p = \frac{1}{12} x^{2} - 14 x + 588$ $p = \frac{1}{12} x^{2} - 14 x + 588$ , $0 \leq x \leq 84$ $0 \leq x \leq 84$
87107	Find the Absolute Max and Min over the Interval	f(x)=5sin(x)+5cos(x) , 0<=x<=2pi	$f (x) = 5 sin (x) + 5 cos (x)$ $f (x) = 5 \sin (x) + 5 \cos (x)$ , $0 \leq x \leq 2 π$ $0 \leq x \leq 2 π$
87108	Find the Absolute Max and Min over the Interval	g(x)=3x^4+8x^3+4	$g (x) = 3 x^{4} + 8 x^{3} + 4$ $g (x) = 3 x^{4} + 8 x^{3} + 4$
87109	Find the Absolute Max and Min over the Interval	g(x)=(x^2+4)/(10x)	$g (x) = \frac{x^{2} + 4}{10 x}$ $g (x) = \frac{x^{2} + 4}{10 x}$
87110	Find the Absolute Max and Min over the Interval	f(x)=( natural log of x)/(x^2)	$f (x) = \frac{ln (x)}{x^{2}}$ $f (x) = \frac{\ln (x)}{x^{2}}$
87111	Find the Absolute Max and Min over the Interval	f(x)=(x^3)/3-(7x^2)/2+10x-5 , [1,4]	$f (x) = \frac{x^{3}}{3} - \frac{7 x^{2}}{2} + 10 x - 5$ $f (x) = \frac{x^{3}}{3} - \frac{7 x^{2}}{2} + 10 x - 5$ , $[1, 4]$ $[1, 4]$
87112	Find the Absolute Max and Min over the Interval	f(x)=sin(x/2) , [pi/2,(3pi)/2]	$f (x) = sin (\frac{x}{2})$ $f (x) = \sin (\frac{x}{2})$ , $[\frac{π}{2}, \frac{3 π}{2}]$ $[\frac{π}{2}, \frac{3 π}{2}]$
87113	Find the Absolute Max and Min over the Interval	f(x)=x^3-12x on -3 , 3	$f (x) = x^{3} - 12 x$ $f (x) = x^{3} - 12 x$ on $- 3$ $- 3$ , $3$ $3$
87114	Find the Absolute Max and Min over the Interval	f(x)=x^2-3x-4	$f (x) = x^{2} - 3 x - 4$ $f (x) = x^{2} - 3 x - 4$
87115	Find the Absolute Max and Min over the Interval	x/(x^2+1)	$\frac{x}{x^{2} + 1}$ $\frac{x}{x^{2} + 1}$
87116	Find the Absolute Max and Min over the Interval	f(x)=(2x^(5/2))/5-(4x^(3/2))/3+(x^2)/2-5 , [0,4]	$f (x) = \frac{2 x^{\frac{5}{2}}}{5} - \frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2} - 5$ $f (x) = \frac{2 x^{\frac{5}{2}}}{5} - \frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2} - 5$ , $[0, 4]$ $[0, 4]$
87117	Find the Absolute Max and Min over the Interval	f(x) = square root of x+3 , 0<=x<=5	$f (x) = \sqrt{x + 3}$ $f (x) = \sqrt{x + 3}$ , $0 \leq x \leq 5$ $0 \leq x \leq 5$
87118	Find the Absolute Max and Min over the Interval	f(x)=-x^2+9 on -3 , 4	$f (x) = - x^{2} + 9$ $f (x) = - x^{2} + 9$ on $- 3$ $- 3$ , $4$ $4$
87119	Find the Absolute Max and Min over the Interval	3x^4+8x^3+4	$3 x^{4} + 8 x^{3} + 4$ $3 x^{4} + 8 x^{3} + 4$
87120	Find the Absolute Max and Min over the Interval	1/x-2/(x^2) , [-2,1]	$\frac{1}{x} - \frac{2}{x^{2}}$ $\frac{1}{x} - \frac{2}{x^{2}}$ , $[- 2, 1]$ $[- 2, 1]$
87121	Find the Absolute Max and Min over the Interval	f(x)=x^a(1-x)^b , 0<=x<=1	$f (x) = x^{a} {(1 - x)}^{b}$ $f (x) = x^{a} {(1 - x)}^{b}$ , $0 \leq x \leq 1$ $0 \leq x \leq 1$
87122	Find the Absolute Max and Min over the Interval	f(x)=\|x\| , given -8<=x<=7	$f (x) = \| x \|$ $f (x) = \| x \|$ , given $- 8 \leq x \leq 7$ $- 8 \leq x \leq 7$
87123	Find the Absolute Max and Min over the Interval	f(x)=cos(x) , [pi,3pi]	$f (x) = cos (x)$ $f (x) = \cos (x)$ , $[π, 3 π]$ $[π, 3 π]$
87124	Find the Absolute Max and Min over the Interval	f(x)=sin(x/2) , [0,4pi]	$f (x) = sin (\frac{x}{2})$ $f (x) = \sin (\frac{x}{2})$ , $[0, 4 π]$ $[0, 4 π]$
87125	Find the Absolute Max and Min over the Interval	f(x)=x(x-4)^2 ; [0,4]	$f (x) = x {(x - 4)}^{2}$ $f (x) = x {(x - 4)}^{2}$ ; $[0, 4]$ $[0, 4]$
87126	Find the Absolute Max and Min over the Interval	f(x)=2x^5-5x^4 on -1 , 3	$f (x) = 2 x^{5} - 5 x^{4}$ $f (x) = 2 x^{5} - 5 x^{4}$ on $- 1$ $- 1$ , $3$ $3$
87127	Find the Absolute Max and Min over the Interval	-x^3+3x^2-6	$- x^{3} + 3 x^{2} - 6$ $- x^{3} + 3 x^{2} - 6$
87128	Find the Absolute Max and Min over the Interval	f(x)=12x^(2/3)+8 , [-8,1]	$f (x) = 12 x^{\frac{2}{3}} + 8$ $f (x) = 12 x^{\frac{2}{3}} + 8$ , $[- 8, 1]$ $[- 8, 1]$
87129	Find the Absolute Max and Min over the Interval	3x^4+4x^3-12x^2+5	$3 x^{4} + 4 x^{3} - 12 x^{2} + 5$ $3 x^{4} + 4 x^{3} - 12 x^{2} + 5$
87130	Find the Absolute Max and Min over the Interval	h(x)=x^3+3x^2+5 on -3 , 2	$h (x) = x^{3} + 3 x^{2} + 5$ $h (x) = x^{3} + 3 x^{2} + 5$ on $- 3$ $- 3$ , $2$ $2$
87131	Find the Absolute Max and Min over the Interval	f(x)=xe^(-2x)	$f (x) = x e^{- 2 x}$ $f (x) = x e^{- 2 x}$
87132	Find the Absolute Max and Min over the Interval	F(theta)=sin(theta+pi/2) , 0<=theta<=(7pi)/4	$F (θ) = sin (θ + \frac{π}{2})$ $F (θ) = \sin (θ + \frac{π}{2})$ , $0 \leq θ \leq \frac{7 π}{4}$ $0 \leq θ \leq \frac{7 π}{4}$
87133	Find the Absolute Max and Min over the Interval	f(x)=x^3-5x-1 ; between 2 and 4	$f (x) = x^{3} - 5 x - 1$ $f (x) = x^{3} - 5 x - 1$ ; between $2$ $2$ and $4$ $4$
87134	Find the Absolute Max and Min over the Interval	f(x)=5sin(x)^2 on [0,pi]	$f (x) = 5 {sin}^{2} (x)$ $f (x) = 5 \sin^{2} (x)$ on $[0, π]$ $[0, π]$
87135	Find the Absolute Max and Min over the Interval	f(x)=x^2-6x	$f (x) = x^{2} - 6 x$ $f (x) = x^{2} - 6 x$
87136	Find the Absolute Max and Min over the Interval	f(x)=sin(x)^2-cos(x) , and 0<=x<=pi	$f (x) = {sin}^{2} (x) - cos (x)$ $f (x) = \sin^{2} (x) - \cos (x)$ , and $0 \leq x \leq π$ $0 \leq x \leq π$
87137	Find the Absolute Max and Min over the Interval	f(x)=2/(x^4-16) on interval -1 , 1.5	$f (x) = \frac{2}{x^{4} - 16}$ $f (x) = \frac{2}{x^{4} - 16}$ on interval $- 1$ $- 1$ , $1.5$ $1.5$
87138	Find the Absolute Max and Min over the Interval	f(x)=x/(x^2+1) on -3 , 3	$f (x) = \frac{x}{x^{2} + 1}$ $f (x) = \frac{x}{x^{2} + 1}$ on $- 3$ $- 3$ , $3$ $3$
87139	Find the Absolute Max and Min over the Interval	f(theta)=1-sin(theta)^2 , [pi/4,pi]	$f (θ) = 1 - {sin}^{2} (θ)$ $f (θ) = 1 - \sin^{2} (θ)$ , $[\frac{π}{4}, π]$ $[\frac{π}{4}, π]$
87140	Find the Absolute Max and Min over the Interval	y=x^3-12x+4	$y = x^{3} - 12 x + 4$ $y = x^{3} - 12 x + 4$
87141	Find the Absolute Max and Min over the Interval	6x^4-32x^3+48x^2-7	$6 x^{4} - 32 x^{3} + 48 x^{2} - 7$
87142	Find the Absolute Max and Min over the Interval	r(t)=t^4+6t^2-2 , [1,4]	$r (t) = t^{4} + 6 t^{2} - 2$ , $[1, 4]$
87143	Find the Absolute Max and Min over the Interval	f(x)=x^3-5x-2 ; between 2 and 3	$f (x) = x^{3} - 5 x - 2$ ; between $2$ and $3$
87144	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x+3 , (-2,2)	$f (x) = x^{3} - 3 x + 3$ , $(- 2, 2)$
87145	Find the Absolute Max and Min over the Interval	f(x)=x^2-x-4 on 0 , 4	$f (x) = x^{2} - x - 4$ on $0$ , $4$
87146	Find the Absolute Max and Min over the Interval	f(t)=(t^2)/(t-8) ; -2<=t<=-1/4	$f (t) = \frac{t^{2}}{t - 8}$ ; $- 2 \leq t \leq - \frac{1}{4}$
87147	Find the Absolute Max and Min over the Interval	f(x)=x^4-8x^2	$f (x) = x^{4} - 8 x^{2}$
87148	Find the Absolute Max and Min over the Interval	f(x)=(x^2-4)^2 on -2 , 2	$f (x) = {(x^{2} - 4)}^{2}$ on $- 2$ , $2$
87149	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x-4 ; between 2 and 4	$f (x) = x^{3} - 3 x - 4$ ; between $2$ and $4$
87150	Find the Absolute Max and Min over the Interval	f(x) = cube root of x-5 ; [-8,-1]	$f (x) = \sqrt[3]{x} - 5$ ; $[- 8, - 1]$
87151	Find the Absolute Max and Min over the Interval	f(x)=4sin(x)^2 on [0,pi]	$f (x) = 4 \sin^{2} (x)$ on $[0, π]$
87152	Find the Absolute Max and Min over the Interval	f(x)=x^4-18x^2+81	$f (x) = x^{4} - 18 x^{2} + 81$
87153	Find the Absolute Max and Min over the Interval	f(x)=x(x-10)^2 ; [0,10]	$f (x) = x {(x - 10)}^{2}$ ; $[0, 10]$
87154	Find the Absolute Max and Min over the Interval	f(x)=x^2+1/x , x>0	$f (x) = x^{2} + \frac{1}{x}$ , $x > 0$
87155	Find the Absolute Max and Min over the Interval	xe^(3x)	$x e^{3 x}$
87156	Find the Absolute Max and Min over the Interval	f(x)=3x^2-x^3	$f (x) = 3 x^{2} - x^{3}$
87157	Find the Absolute Max and Min over the Interval	y=3^x , [0,4]	$y = 3^{x}$ , $[0, 4]$
87158	Find the Absolute Max and Min over the Interval	f(x)=4x^3-4x-1 ; between 1 and 3	$f (x) = 4 x^{3} - 4 x - 1$ ; between $1$ and $3$
87159	Find the Absolute Max and Min over the Interval	y=sin(x)	$y = \sin (x)$
87160	Find the Absolute Max and Min over the Interval	f(x)=5x^3-4x-4 ; between 1 and 5	$f (x) = 5 x^{3} - 4 x - 4$ ; between $1$ and $5$
87161	Find the Absolute Max and Min over the Interval	-3x^4-8x^3-6x^2+1	$- 3 x^{4} - 8 x^{3} - 6 x^{2} + 1$
87162	Find the Absolute Max and Min over the Interval	f(x)=x^3-10x^2+27x-18	$f (x) = x^{3} - 10 x^{2} + 27 x - 18$
87163	Find the Absolute Max and Min over the Interval	f(x) = square root of 9-x^2	$f (x) = \sqrt{9 - x^{2}}$
87164	Find the Absolute Max and Min over the Interval	f(x) = square root of x+5	$f (x) = \sqrt{x + 5}$
87165	Find the Absolute Max and Min over the Interval	f(x)=4x^3-3x-4 ; between 1 and 6	$f (x) = 4 x^{3} - 3 x - 4$ ; between $1$ and $6$
87166	Find the Absolute Max and Min over the Interval	f(x)=(2x^(5/2))/5-(4x^(3/2))/3+(x^2)/2-4 , [0,3]	$f (x) = \frac{2 x^{\frac{5}{2}}}{5} - \frac{4 x^{\frac{3}{2}}}{3} + \frac{x^{2}}{2} - 4$ , $[0, 3]$
87167	Find the Absolute Max and Min over the Interval	y=3x+3sin(x) , 0<=x<=2pi	$y = 3 x + 3 \sin (x)$ , $0 \leq x \leq 2 π$
87168	Find the Absolute Max and Min over the Interval	h(x)=-3x^4+8x^3+18x^2	$h (x) = - 3 x^{4} + 8 x^{3} + 18 x^{2}$
87169	Find the Absolute Max and Min over the Interval	f(x)=-(3/5)x^5-2x^3+3x-12 , [-4,3]	$f (x) = - (\frac{3}{5}) x^{5} - 2 x^{3} + 3 x - 12$ , $[- 4, 3]$
87170	Find the Absolute Max and Min over the Interval	f(x)=3x^(2/3)-2x	$f (x) = 3 x^{\frac{2}{3}} - 2 x$
87171	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x^2+3 , (-1,3)	$f (x) = x^{3} - 3 x^{2} + 3$ , $(- 1, 3)$
87172	Find the Absolute Max and Min over the Interval	y=6-2x^2 , [-3,3]	$y = 6 - 2 x^{2}$ , $[- 3, 3]$
87173	Find the Absolute Max and Min over the Interval	f(theta)=2cos(theta)+cos(theta)^2 , 0<=theta<=2pi	$f (θ) = 2 \cos (θ) + \cos^{2} (θ)$ , $0 \leq θ \leq 2 π$
87174	Find the Absolute Max and Min over the Interval	f(x)=3cos(x)^2 , [pi/4,pi]	$f (x) = 3 \cos^{2} (x)$ , $[\frac{π}{4}, π]$
87175	Find the Absolute Max and Min over the Interval	f(x)=cos(x)^2 on [0,pi]	$f (x) = \cos^{2} (x)$ on $[0, π]$
87176	Find the Absolute Max and Min over the Interval	f(x)=cos(x+pi/4) , 0<=x<=2pi	$f (x) = \cos (x + \frac{π}{4})$ , $0 \leq x \leq 2 π$
87177	Find the Absolute Max and Min over the Interval	f(x)=(x^3)/3-(7x^2)/2+10x-5 , [1,4]	$f (x) = \frac{x^{3}}{3} - \frac{7 x^{2}}{2} + 10 x - 5$ , $[1, 4]$
87178	Find the Absolute Max and Min over the Interval	f(x)=(x^2-1)^3	$f (x) = {(x^{2} - 1)}^{3}$
87179	Find the Absolute Max and Min over the Interval	f(x) = square root of x-5-4 ; 10<=x<=21	$f (x) = \sqrt{x - 5} - 4$ ; $10 \leq x \leq 21$
87180	Find the Absolute Max and Min over the Interval	f(x)=2cos(x)^2 on [0,pi]	$f (x) = 2 \cos^{2} (x)$ on $[0, π]$
87181	Find the Absolute Max and Min over the Interval	h(x)=- cube root of x , -1<=x<=27	$h (x) = - \sqrt[3]{x}$ , $- 1 \leq x \leq 27$
87182	Find the Absolute Max and Min over the Interval	f(x)=x^4+8x^3+18x^2+4 , [-4,1]	$f (x) = x^{4} + 8 x^{3} + 18 x^{2} + 4$ , $[- 4, 1]$
87183	Find the Absolute Max and Min over the Interval	f(x)=2x^3+21x^2+36x , [-8,0]	$f (x) = 2 x^{3} + 21 x^{2} + 36 x$ , $[- 8, 0]$
87184	Find the Absolute Max and Min over the Interval	f(x)=\|x\| , given square root of 5<=x< = square root of 13	$f (x) = \| x \|$ , given $\sqrt{5} \leq x \leq \sqrt{13}$
87185	Find the Absolute Max and Min over the Interval	h(x)=-x^3+4	$h (x) = - x^{3} + 4$
87186	Find the Absolute Max and Min over the Interval	f(x)=-x^4+8x^2-8	$f (x) = - x^{4} + 8 x^{2} - 8$
87187	Find the Absolute Max and Min over the Interval	f(x)=sin(x)	$f (x) = \sin (x)$
87188	Find the Absolute Max and Min over the Interval	x^3-12x	$x^{3} - 12 x$
87189	Find the Absolute Max and Min over the Interval	f(x)=x^(2/3) ; [-1,1]	$f (x) = x^{\frac{2}{3}}$ ; $[- 1, 1]$
87190	Find the Absolute Max and Min over the Interval	f(x)=x^4+4x^3+4x^2 on -2 , 1	$f (x) = x^{4} + 4 x^{3} + 4 x^{2}$ on $- 2$ , $1$
87191	Find the Absolute Max and Min over the Interval	y=7x+7sin(x) , 0<=x<=2pi	$y = 7 x + 7 \sin (x)$ , $0 \leq x \leq 2 π$
87192	Find the Absolute Max and Min over the Interval	f(x)=x^2-x-6 on 0 , 6	$f (x) = x^{2} - x - 6$ on $0$ , $6$
87193	Find the Absolute Max and Min over the Interval	g(t)=(t^2)/(t^2+3) , [-1,1]	$g (t) = \frac{t^{2}}{t^{2} + 3}$ , $[- 1, 1]$
87194	Find the Absolute Max and Min over the Interval	y=2(1/5)^x , [-2,3]	$y = 2 {(\frac{1}{5})}^{x}$ , $[- 2, 3]$
87195	Find the Absolute Max and Min over the Interval	f(x)=5- square root of x-5 ; 5<=x<=9	$f (x) = 5 - \sqrt{x - 5}$ ; $5 \leq x \leq 9$
87196	Find the Absolute Max and Min over the Interval	f(x)=x^3-3x+1 on [0,2]	$f (x) = x^{3} - 3 x + 1$ on $[0, 2]$
87197	Find the Absolute Max and Min over the Interval	g(x)=- square root of 5-x^2 , - square root of 5<=x<=0	$g (x) = - \sqrt{5 - x^{2}}$ , $- \sqrt{5} \leq x \leq 0$
87198	Find the Absolute Max and Min over the Interval	f(x)=x^3-3/2x^2-6x , [-2,3]	$f (x) = x^{3} - \frac{3}{2} x^{2} - 6 x$ , $[- 2, 3]$
87199	Find the Absolute Max and Min over the Interval	f(x)=-2x^3+15x^2-24x on 0 , 5	$f (x) = - 2 x^{3} + 15 x^{2} - 24 x$ on $0$ , $5$
87200	Find the Absolute Max and Min over the Interval	f(x)=\|x+1\|	$f (x) = \| x + 1 \|$