Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
86401	Find the Tangent Line at (-6,-2)	f(x)=1/3x^2+3x+4 at (-6,-2)	$f (x) = \frac{1}{3} x^{2} + 3 x + 4$ at $(- 6, - 2)$
86402	Find the Tangent Line at (3,3)	f(x)=(4x)/(x^2-5) ; (3,3)	$f (x) = \frac{4 x}{x^{2} - 5}$ ; $(3, 3)$
86403	Find the Tangent Line at (-2,-5)	f(x)=x^3+x+5 ;, (-2,-5)	$f (x) = x^{3} + x + 5$ ;, $(- 2, - 5)$
86404	Find the Tangent Line at (-9,-2/9)	f(x)=2/x at (-9,-2/9)	$f (x) = \frac{2}{x}$ at $(- 9, - \frac{2}{9})$
86405	Find the Tangent Line at (0,5)	y=5e^x+x , (0,5)	$y = 5 e^{x} + x$ , $(0, 5)$
86406	Find the Tangent Line at (1,0)	y = natural log of x^(9/2) ; (1,0)	$y = \ln (x^{\frac{9}{2}})$ ; $(1, 0)$
86407	Find the Tangent Line at x=2	f(x)=( natural log of x)^3 at x=2	$f (x) = \ln^{3} (x)$ at $x = 2$
86408	Find the Tangent Line at (0,2)	f(x)=2e^xcos(x) , (0,2)	$f (x) = 2 e^{x} \cos (x)$ , $(0, 2)$
86409	Find the Tangent Line at (1,-1)	y=x^5-3x^3-2x+3 ; (1,-1)	$y = x^{5} - 3 x^{3} - 2 x + 3$ ; $(1, - 1)$
86410	Find the Tangent Line at (9,0)	y = natural log of x^2-9x+1 , (9,0)	$y = \ln (x^{2} - 9 x + 1)$ , $(9, 0)$
86411	Find the Tangent Line at (0,3)	f(x)=3e^xcos(x) , (0,3)	$f (x) = 3 e^{x} \cos (x)$ , $(0, 3)$
86412	Find the Tangent Line at (π/4,1)	f(x)=tan(x) , (pi/4,1)	$f (x) = \tan (x)$ , $(\frac{π}{4}, 1)$
86413	Find the Tangent Line at (1,1)	f(x)=1/(x^3) at the point (1,1)	$f (x) = \frac{1}{x^{3}}$ at the point $(1, 1)$
86414	Find the Tangent Line at (1,-1)	f(x)=-1/x at (1,-1)	$f (x) = - \frac{1}{x}$ at $(1, - 1)$
86415	Find the Tangent Line at x=1	f(x)=6+ natural log of x ; x=1	$f (x) = 6 + \ln (x)$ ; $x = 1$
86416	Find the Tangent Line at x=-1	f(x)=2x^3 ; x=-1	$f (x) = 2 x^{3}$ ; $x = - 1$
86417	Find the Tangent Line at x=-π/2	y=cot(x) ; x=-pi/2	$y = \cot (x)$ ; $x = - \frac{π}{2}$
86418	Find the Tangent Line at x=3	y=(x^2-9x)/(3x-x^3) at x=3	$y = \frac{x^{2} - 9 x}{3 x - x^{3}}$ at $x = 3$
86419	Find the Tangent Line at (0,4)	f(x)=4e^xcos(x) , (0,4)	$f (x) = 4 e^{x} \cos (x)$ , $(0, 4)$
86420	Find the Tangent Line at (3,1)	x^2y^8=9 , (3,1)	$x^{2} y^{8} = 9$ , $(3, 1)$
86421	Find the Tangent Line at x=1	f(x)=x^4-25x^2+144 ; x=1	$f (x) = x^{4} - 25 x^{2} + 144$ ; $x = 1$
86422	Find the Tangent Line at (1,1)	f(x)=1/(x^6) at (1,1)	$f (x) = \frac{1}{x^{6}}$ at $(1, 1)$
86423	Find the Tangent Line at (0,9)	y=(e^(2x)-4)^2 , (0,9)	$y = {(e^{2 x} - 4)}^{2}$ , $(0, 9)$
86424	Find the Tangent Line at (-2,-16)	y=2x^3 , (-2,-16)	$y = 2 x^{3}$ , $(- 2, - 16)$
86425	Find the Tangent Line at (1,e)	y=x^2e^x-2xe^x+2e^x , (1,e)	$y = x^{2} e^{x} - 2 x e^{x} + 2 e^{x}$ , $(1, e)$
86426	Find the Tangent Line at (2,1)	y=(2x)/(x+2) , (2,1)	$y = \frac{2 x}{x + 2}$ , $(2, 1)$
86427	Find the Tangent Line at x=2	y=x^2-6x+9 at x=2	$y = x^{2} - 6 x + 9$ at $x = 2$
86428	Find the Tangent Line at x=0	f(x)=4x^2+2x-1 at x=0	$f (x) = 4 x^{2} + 2 x - 1$ at $x = 0$
86429	Find the Tangent Line at (1,6)	y=3x^3-x^2+4 , (1,6)	$y = 3 x^{3} - x^{2} + 4$ , $(1, 6)$
86430	Find the Tangent Line at x=1	f(x)=x^4-10x^2+9 ; x=1	$f (x) = x^{4} - 10 x^{2} + 9$ ; $x = 1$
86431	Find the Tangent Line at (0,4)	y=4e^xcos(x) , (0,4)	$y = 4 e^{x} \cos (x)$ , $(0, 4)$
86432	Find the Tangent Line at x=3/4⋅π	f(x)=-2sin(x) at x=3/4pi	$f (x) = - 2 \sin (x)$ at $x = \frac{3}{4} π$
86433	Find the Tangent Line at (1,1/e)	y=x^4e^(-x) , (1,1/e)	$y = x^{4} e^{- x}$ , $(1, \frac{1}{e})$
86434	Find the Tangent Line at (0,-3)	y=-3/((3x^2+1)^3) ; (0,-3)	$y = \frac{- 3}{{(3 x^{2} + 1)}^{3}}$ ; $(0, - 3)$
86435	Find the Tangent Line at (8,0)	y = natural log of x^2-8x+1 , (8,0)	$y = \ln (x^{2} - 8 x + 1)$ , $(8, 0)$
86436	Find the Tangent Line at (-2,-3)	f(x)=x^3+x+7 ;, (-2,-3)	$f (x) = x^{3} + x + 7$ ;, $(- 2, - 3)$
86437	Find the Tangent Line at (9,7)	(y-3)^2=4(x-5) , (9,7)	${(y - 3)}^{2} = 4 (x - 5)$ , $(9, 7)$
86438	Find the Tangent Line at x=4	y=(x^2-16x)/(4x-x^3) at x=4	$y = \frac{x^{2} - 16 x}{4 x - x^{3}}$ at $x = 4$
86439	Find the Tangent Line at P=(π/3,-1)	y=sec(x)-6cos(x) , P=(pi/3,-1)	$y = \sec (x) - 6 \cos (x)$ , $P = (\frac{π}{3}, - 1)$
86440	Find the Tangent Line at (7,2/7)	f(x)=2/x at (7,2/7)	$f (x) = \frac{2}{x}$ at $(7, \frac{2}{7})$
86441	Find the Tangent Line at x=6	f(x)=( natural log of x)^2 at x=6	$f (x) = \ln^{2} (x)$ at $x = 6$
86442	Find the Tangent Line at (1,3)	y=4x^2-x^3 , (1,3)	$y = 4 x^{2} - x^{3}$ , $(1, 3)$
86443	Find the Tangent Line at (1/2,π/2)	y=3arcsin(x) , (1/2,pi/2)	$y = 3 \arcsin (x)$ , $(\frac{1}{2}, \frac{π}{2})$
86444	Find the Tangent Line at (-8,-3/8)	f(x)=3/x at (-8,-3/8)	$f (x) = \frac{3}{x}$ at $(- 8, - \frac{3}{8})$
86445	Find the Tangent Line at x=2	f(x)=((x-1)^2-x)^2 at x=2	$f (x) = {({(x - 1)}^{2} - x)}^{2}$ at $x = 2$
86446	Find the Tangent Line at (3,-5)	y=(x+2)/(x-4) , (3,-5)	$y = \frac{x + 2}{x - 4}$ , $(3, - 5)$
86447	Find the Tangent Line at (1,2)	y=(4x)/(x^2+1) at the origin and at the point (1,2)	$y = \frac{4 x}{x^{2} + 1}$ at the origin and at the point $(1, 2)$
86448	Find the Tangent Line at (2,6)	y^2-x^2y-6x=0 , (2,6)	$y^{2} - x^{2} y - 6 x = 0$ , $(2, 6)$
86449	Find the Tangent Line at (9,-1)	(y-3)^2=4(x-5) , (9,-1)	${(y - 3)}^{2} = 4 (x - 5)$ , $(9, - 1)$
86450	Find the Tangent Line at (3,9)	y=x^2 , (3,9)	$y = x^{2}$ , $(3, 9)$
86451	Find the Tangent Line at (-2,-7)	f(x)=x^3+x+3 ;, (-2,-7)	$f (x) = x^{3} + x + 3$ ;, $(- 2, - 7)$
86452	Find the Tangent Line at x=5	f(x)=( natural log of x)^2 at x=5	$f (x) = \ln^{2} (x)$ at $x = 5$
86453	Find the Tangent Line at x=2	f(x)=( natural log of x)^4 at x=2	$f (x) = \ln^{4} (x)$ at $x = 2$
86454	Find the Tangent Line at (4,4)	f(x)=(10x)/(x^2-6) ; (4,4)	$f (x) = \frac{10 x}{x^{2} - 6}$ ; $(4, 4)$
86455	Find the Tangent Line at x=-1	f(x)=3x^3 ; x=-1	$f (x) = 3 x^{3}$ ; $x = - 1$
86456	Find the Tangent Line at x=9	f(x)=( natural log of x)^3 at x=9	$f (x) = \ln^{3} (x)$ at $x = 9$
86457	Find the Tangent Line at (0,4)	y=4e^xcos(x) , (0,4)	$y = 4 e^{x} \cos (x)$ , $(0, 4)$
86458	Find the Tangent Line at (0,5)	y=10/(1+e^(-x)) , (0,5)	$y = \frac{10}{1 + e^{- x}}$ , $(0, 5)$
86459	Find the Tangent Line at (1,2)	y=3x^2-2x+1 at (1,2)	$y = 3 x^{2} - 2 x + 1$ at $(1, 2)$
86460	Find the Tangent Line at (2,21)	y=3x^3-x^2+1 , (2,21)	$y = 3 x^{3} - x^{2} + 1$ , $(2, 21)$
86461	Find the Tangent Line at (1,1)	f(x)=x^5 , (1,1)	$f (x) = x^{5}$ , $(1, 1)$
86462	Find the Tangent Line at (0,9)	y=9e^xcos(x) , (0,9)	$y = 9 e^{x} \cos (x)$ , $(0, 9)$
86463	Find the Tangent Line at (2,29)	y=3x^3-x^2+9 , (2,29)	$y = 3 x^{3} - x^{2} + 9$ , $(2, 29)$
86464	Find the Tangent Line at (4/3,8/3)	x^3+y^3-6xy=0 , (4/3,8/3)	$x^{3} + y^{3} - 6 x y = 0$ , $(\frac{4}{3}, \frac{8}{3})$
86465	Find the Tangent Line at (-1,4)	y=(-8x)/(x^2+1) at the origin and at the point (-1,4)	$y = \frac{- 8 x}{x^{2} + 1}$ at the origin and at the point $(- 1, 4)$
86466	Find the Tangent Line at (1,2)	4x^2+2y^2=12 , (1,2)	$4 x^{2} + 2 y^{2} = 12$ , $(1, 2)$
86467	Find the Tangent Line at (1,3)	x^2+y^2=10 , (1,3)	$x^{2} + y^{2} = 10$ , $(1, 3)$
86468	Find the Tangent Line at x=2	f(x)=x^4-25x^2+144 ; x=2	$f (x) = x^{4} - 25 x^{2} + 144$ ; $x = 2$
86469	Find the Tangent Line at x=1/9	f(x) = square root of x , x=1/9	$f (x) = \sqrt{x}$ , $x = \frac{1}{9}$
86470	Find the Tangent Line at x=-2	f(x)=-x^3+4x-2 at x=-2	$f (x) = - x^{3} + 4 x - 2$ at $x = - 2$
86471	Find the Tangent Line at (4,4)	g(x)=(6x)/(x+2) at (4,4)	$g (x) = \frac{6 x}{x + 2}$ at $(4, 4)$
86472	Find the Tangent Line at (-1,8)	y=(x^2-x)^3 at (-1,8)	$y = {(x^{2} - x)}^{3}$ at $(- 1, 8)$
86473	Find the Tangent Line at x=-π/4	f(x)=-5cot(x)-(5pi)/2-4 at x=-pi/4	$f (x) = - 5 \cot (x) - \frac{5 π}{2} - 4$ at $x = - \frac{π}{4}$
86474	Find the Tangent Line at (1,3)	y=(6x)/(x^2+1) at the origin and at the point (1,3)	$y = \frac{6 x}{x^{2} + 1}$ at the origin and at the point $(1, 3)$
86475	Find the Tangent Line at (2,2)	g(x)=(3x)/(x+1) at (2,2)	$g (x) = \frac{3 x}{x + 1}$ at $(2, 2)$
86476	Find the Tangent Line at (-4,17)	y=x^2+1 , (-4,17)	$y = x^{2} + 1$ , $(- 4, 17)$
86477	Find the Tangent Line at (0,-2)	y^2(y^2-4)=x^2(x^2-5) , (0,-2)	$y^{2} (y^{2} - 4) = x^{2} (x^{2} - 5)$ , $(0, - 2)$
86478	Find the Tangent Line at x=1	f(x)=x^4(3-x)^2 ; x=1	$f (x) = x^{4} {(3 - x)}^{2}$ ; $x = 1$
86479	Find the Tangent Line at (-1,1)	(x^2+y^2)^2=4x^2y , (-1,1)	${(x^{2} + y^{2})}^{2} = 4 x^{2} y$ , $(- 1, 1)$
86480	Find the Tangent Line at x=-2	f(x)=x^4-25x^2+144 ; x=-2	$f (x) = x^{4} - 25 x^{2} + 144$ ; $x = - 2$
86481	Find the Tangent Line at (4,9)	square root of x+ square root of y=5 , (4,9)	$\sqrt{x} + \sqrt{y} = 5$ , $(4, 9)$
86482	Find the Tangent Line at x=0	f(x) = square root of x+9 at the point where x=0	$f (x) = \sqrt{x + 9}$ at the point where $x = 0$
86483	Find the Tangent Line at x=7	f(x)=( natural log of x)^5 at x=7	$f (x) = \ln^{5} (x)$ at $x = 7$
86484	Find the Tangent Line at x=4	f(x)=( natural log of x)^4 at x=4	$f (x) = \ln^{4} (x)$ at $x = 4$
86485	Find the Tangent Line at (π/2,5π)	y=10xsin(x) , (pi/2,5pi)	$y = 10 x \sin (x)$ , $(\frac{π}{2}, 5 π)$
86486	Find the Tangent Line at (-1,3)	y=(-6x)/(x^2+1) at the origin and at the point (-1,3)	$y = \frac{- 6 x}{x^{2} + 1}$ at the origin and at the point $(- 1, 3)$
86487	Find the Tangent Line at (0,6)	y=6e^xcos(x) , (0,6)	$y = 6 e^{x} \cos (x)$ , $(0, 6)$
86488	Find the Tangent Line at x=1	y=5x^2-7 at x=1	$y = 5 x^{2} - 7$ at $x = 1$
86489	Find the Tangent Line at (1,3)	y=4-x^2 ; (1,3)	$y = 4 - x^{2}$ ; $(1, 3)$
86490	Find the Tangent Line at (64,16)	x^2=y^3 ; (64,16)	$x^{2} = y^{3}$ ; $(64, 16)$
86491	Find the Tangent Line at (π/2,5π)	y=10xsin(x) , (pi/2,5pi)	$y = 10 x \sin (x)$ , $(\frac{π}{2}, 5 π)$
86492	Find the Tangent Line at (π,-1)	y=(1+sin(x))/(cos(x)) , (pi,-1)	$y = \frac{1 + \sin (x)}{\cos (x)}$ , $(π, - 1)$
86493	Find the Tangent Line at x=2	f(x)=x^4-20x^2+64 ; x=2	$f (x) = x^{4} - 20 x^{2} + 64$ ; $x = 2$
86494	Find the Tangent Line at x=3	f(x)=( natural log of x)^5 at x=3	$f (x) = \ln^{5} (x)$ at $x = 3$
86495	Find the Tangent Line at (1,2)	x^2+2xy-y^2+x=2 , (1,2)	$x^{2} + 2 x y - y^{2} + x = 2$ , $(1, 2)$
86496	Find the Tangent Line at (-2,0)	f(x)=x^3+8 , (-2,0)	$f (x) = x^{3} + 8$ , $(- 2, 0)$
86497	Find the Tangent Line at (-1,-2)	y=(4x)/(x^2+1) at the origin and at the point (-1,-2)	$y = \frac{4 x}{x^{2} + 1}$ at the origin and at the point $(- 1, - 2)$
86498	Find the Tangent Line at (3,3)	f(x)=(8x)/(x^2-1) ; (3,3)	$f (x) = \frac{8 x}{x^{2} - 1}$ ; $(3, 3)$
86499	Find the Tangent Line at (0,7)	f(x)=7e^xcos(x) , (0,7)	$f (x) = 7 e^{x} \cos (x)$ , $(0, 7)$
86500	Find the Tangent Line at (1,5)	y=3x^3-x^2+3 , (1,5)	$y = 3 x^{3} - x^{2} + 3$ , $(1, 5)$