Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
86101	Find the Tangent Line at (2,2)	y=(4x)/(x+2) , (2,2)	$y = \frac{4 x}{x + 2}$ , $(2, 2)$
86102	Find the Tangent Line at (4π,0)	y=sin(sin(x)) , (4pi,0)	$y = \sin (\sin (x))$ , $(4 π, 0)$
86103	Find the Tangent Line at (1,-27)	f(x)=(x-4)(x^2+8) , (1,-27)	$f (x) = (x - 4) (x^{2} + 8)$ , $(1, - 27)$
86104	Find the Tangent Line at (1,-14)	f(x)=(x-3)(x^2+6) , (1,-14)	$f (x) = (x - 3) (x^{2} + 6)$ , $(1, - 14)$
86105	Find the Tangent Line at (2,8)	y=x^3 , (2,8)	$y = x^{3}$ , $(2, 8)$
86106	Find the Tangent Line at (1,0)	y=x-x^3 , (1,0)	$y = x - x^{3}$ , $(1, 0)$
86107	Find the Tangent Line at (3,20)	y=x^3-3x+2 , (3,20)	$y = x^{3} - 3 x + 2$ , $(3, 20)$
86108	Find the Tangent Line at (9,36)	y=12 square root of x , (9,36)	$y = 12 \sqrt{x}$ , $(9, 36)$
86109	Find the Tangent Line at (1,0)	y = natural log of x^(7/2) ; (1,0)	$y = \ln (x^{\frac{7}{2}})$ ; $(1, 0)$
86110	Find the Tangent Line at (-1,-1)	y=x^3 , (-1,-1)	$y = x^{3}$ , $(- 1, - 1)$
86111	Find the Tangent Line at x=2	f(x) = square root of x^2+45 ; x=2	$f (x) = \sqrt{x^{2} + 45}$ ; $x = 2$
86112	Find the Tangent Line at x=4	f(x) = square root of x^2+33 ; x=4	$f (x) = \sqrt{x^{2} + 33}$ ; $x = 4$
86113	Find the Tangent Line at (1,8)	y=x^4+8x^2-x , (1,8)	$y = x^{4} + 8 x^{2} - x$ , $(1, 8)$
86114	Find the Tangent Line at (1,0)	f(x)=e^(-x) natural log of x , (1,0)	$f (x) = e^{- x} \ln (x)$ , $(1, 0)$
86115	Find the Tangent Line at x=-1	f(x)=(x^7)/7-7/(x^7) at x=-1	$f (x) = \frac{x^{7}}{7} - \frac{7}{x^{7}}$ at $x = - 1$
86116	Find the Tangent Line at (4,8)	y=4 square root of x , (4,8)	$y = 4 \sqrt{x}$ , $(4, 8)$
86117	Find the Tangent Line at (9,3)	y = square root of x , (9,3)	$y = \sqrt{x}$ , $(9, 3)$
86118	Find the Tangent Line at (0,9)	y=(e^(3x)-4)^2 , (0,9)	$y = {(e^{3 x} - 4)}^{2}$ , $(0, 9)$
86119	Find the Tangent Line at (1,1)	y=9x-8 square root of x , (1,1)	$y = 9 x - 8 \sqrt{x}$ , $(1, 1)$
86120	Find the Tangent Line at (4,2√(3))	x^2y^2-9x^2-4y^2=0 , (4,2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(4, 2 \sqrt{3})$
86121	Find the Tangent Line at (0,-2)	y^2(y^2-4)=x^2(x^2-5) , (0,-2)	$y^{2} (y^{2} - 4) = x^{2} (x^{2} - 5)$ , $(0, - 2)$
86122	Find the Tangent Line at (4,9)	square root of x+ square root of y=5 , (4,9)	$\sqrt{x} + \sqrt{y} = 5$ , $(4, 9)$
86123	Find the Tangent Line at (1,6)	f(x)=7x^2-x^3 , (1,6)	$f (x) = 7 x^{2} - x^{3}$ , $(1, 6)$
86124	Find the Tangent Line at (4,32)	y=16 square root of x , (4,32)	$y = 16 \sqrt{x}$ , $(4, 32)$
86125	Find the Tangent Line at (1,1/2)	y=1/(1+x^2) , (1,1/2)	$y = \frac{1}{1 + x^{2}}$ , $(1, \frac{1}{2})$
86126	Find the Tangent Line at (1,2)	y^2=x^3+3x^2 , (1,2)	$y^{2} = x^{3} + 3 x^{2}$ , $(1, 2)$
86127	Find the Tangent Line at (9,3)	f(x) = square root of x , (9,3)	$f (x) = \sqrt{x}$ , $(9, 3)$
86128	Find the Tangent Line at x=6	f(x) = square root of x^2+13 ; x=6	$f (x) = \sqrt{x^{2} + 13}$ ; $x = 6$
86129	Find the Tangent Line at (1,1)	y=(2x)/(x+1) , (1,1)	$y = \frac{2 x}{x + 1}$ , $(1, 1)$
86130	Find the Tangent Line at x=1	f(x)=(10x-6)^(1/2) , x=1	$f (x) = {(10 x - 6)}^{\frac{1}{2}}$ , $x = 1$
86131	Find the Tangent Line at (4,54)	y=x^3-3x+2 , (4,54)	$y = x^{3} - 3 x + 2$ , $(4, 54)$
86132	Find the Tangent Line at x=1	f(x)=(6x-5)^(1/2) , x=1	$f (x) = {(6 x - 5)}^{\frac{1}{2}}$ , $x = 1$
86133	Find the Tangent Line at (1,-2)	y=-2x^3 , (1,-2)	$y = - 2 x^{3}$ , $(1, - 2)$
86134	Find the Tangent Line at (-4,2√(3))	x^2y^2-9x^2-4y^2=0 , (-4,2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(- 4, 2 \sqrt{3})$
86135	Find the Tangent Line at (5,3)	x^2-xy-y^2=1 , (5,3)	$x^{2} - x y - y^{2} = 1$ , $(5, 3)$
86136	Find the Tangent Line at (1,1)	y=(4x)/(x+3) , (1,1)	$y = \frac{4 x}{x + 3}$ , $(1, 1)$
86137	Find the Tangent Line at (4,-2√(3))	x^2y^2-9x^2-4y^2=0 , (4,-2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(4, - 2 \sqrt{3})$
86138	Find the Tangent Line at (1,1)	y=7x-6 square root of x , (1,1)	$y = 7 x - 6 \sqrt{x}$ , $(1, 1)$
86139	Find the Tangent Line at x=4	f(x) = square root of 4x+7 , x=4	$f (x) = \sqrt{4 x + 7}$ , $x = 4$
86140	Find the Tangent Line at (-1,0)	y=2x^3-2x at the point (-1,0)	$y = 2 x^{3} - 2 x$ at the point $(- 1, 0)$
86141	Find the Tangent Line at (2,5)	y=9-x^2 ; (2,5)	$y = 9 - x^{2}$ ; $(2, 5)$
86142	Find the Tangent Line at (-2,8)	y=-x^3 , (-2,8)	$y = - x^{3}$ , $(- 2, 8)$
86143	Find the Tangent Line at (3,3)	y=(4x)/(x+1) , (3,3)	$y = \frac{4 x}{x + 1}$ , $(3, 3)$
86144	Find the Tangent Line at (2,6)	y=x^3-3x+4 at (2,6)	$y = x^{3} - 3 x + 4$ at $(2, 6)$
86145	Find the Tangent Line at (2,6)	y=x^3-2x+2 , (2,6)	$y = x^{3} - 2 x + 2$ , $(2, 6)$
86146	Find the Tangent Line at (-1,1/2)	y=1/(1+x^2) , (-1,1/2)	$y = \frac{1}{(1 + x^{2})}$ , $(- 1, \frac{1}{2})$
86147	Find the Tangent Line at (1,e)	y=(e^x)/x , (1,e)	$y = \frac{e^{x}}{x}$ , $(1, e)$
86148	Find the Tangent Line at (4,40)	y=20 square root of x , (4,40)	$y = 20 \sqrt{x}$ , $(4, 40)$
86149	Find the Tangent Line at x=3	f(x)=(6x-2)^(1/2) , x=3	$f (x) = {(6 x - 2)}^{\frac{1}{2}}$ , $x = 3$
86150	Find the Tangent Line at (2,-8)	y=-x^3 , (2,-8)	$y = - x^{3}$ , $(2, - 8)$
86151	Find the Tangent Line at (4,58)	y=x^3-2x+2 , (4,58)	$y = x^{3} - 2 x + 2$ , $(4, 58)$
86152	Find the Tangent Line at (9,4)	square root of x+ square root of y=5 , (9,4)	$\sqrt{x} + \sqrt{y} = 5$ , $(9, 4)$
86153	Find the Tangent Line at (-1,0)	y=5x^3-5x at the point (-1,0)	$y = 5 x^{3} - 5 x$ at the point $(- 1, 0)$
86154	Find the Tangent Line at (1,1)	y=(2x)/(x^2+1) , (1,1)	$y = \frac{2 x}{x^{2} + 1}$ , $(1, 1)$
86155	Find the Tangent Line at (1,3)	y=7x-4 square root of x , (1,3)	$y = 7 x - 4 \sqrt{x}$ , $(1, 3)$
86156	Find the Tangent Line at (-1,2)	y=-2x^3 , (-1,2)	$y = - 2 x^{3}$ , $(- 1, 2)$
86157	Find the Tangent Line at (1,4)	f(x)=5x^2-x^3 , (1,4)	$f (x) = 5 x^{2} - x^{3}$ , $(1, 4)$
86158	Find the Tangent Line at (1,3)	y=9x-6 square root of x , (1,3)	$y = 9 x - 6 \sqrt{x}$ , $(1, 3)$
86159	Find the Tangent Line at (-2,-1)	f(x)=-1/4x^2 ;, (-2,-1)	$f (x) = - \frac{1}{4} x^{2}$ ;, $(- 2, - 1)$
86160	Find the Tangent Line at (1,0)	y=2x^3-2x at the point (1,0)	$y = 2 x^{3} - 2 x$ at the point $(1, 0)$
86161	Find the Tangent Line at (1,1)	x^2+xy+y^2=3 , (1,1)	$x^{2} + x y + y^{2} = 3$ , $(1, 1)$
86162	Find the Tangent Line at (-2,32)	g(x)=2x^4 ; (-2,32)	$g (x) = 2 x^{4}$ ; $(- 2, 32)$
86163	Find the Tangent Line at (0,3)	y=3e^x+x , (0,3)	$y = 3 e^{x} + x$ , $(0, 3)$
86164	Find the Tangent Line at x=π/2	y=8sin(x)cos(x) ; x=pi/2	$y = 8 \sin (x) \cos (x)$ ; $x = \frac{π}{2}$
86165	Find the Tangent Line at (1,7)	y=8x-x^2 , (1,7)	$y = 8 x - x^{2}$ , $(1, 7)$
86166	Find the Tangent Line at (-4,-2√(3))	x^2y^2-9x^2-4y^2=0 , (-4,-2 square root of 3)	$x^{2} y^{2} - 9 x^{2} - 4 y^{2} = 0$ , $(- 4, - 2 \sqrt{3})$
86167	Find the Tangent Line at (1,2)	y = square root of 3+x^3 , (1,2)	$y = \sqrt{3 + x^{3}}$ , $(1, 2)$
86168	Find the Tangent Line at x=-1	f(x)=x^3 ; x=-1	$f (x) = x^{3}$ ; $x = - 1$
86169	Find the Tangent Line at (2,2)	y = fifth root of 2x^3+8x , (2,2)	$y = \sqrt[5]{2 x^{3} + 8 x}$ , $(2, 2)$
86170	Find the Tangent Line at (1,2)	y=2 square root of x , (1,2)	$y = 2 \sqrt{x}$ , $(1, 2)$
86171	Find the Tangent Line at (-1,2)	y = square root of 5+x^3 , (-1,2)	$y = \sqrt{5 + x^{3}}$ , $(- 1, 2)$
86172	Find the Tangent Line at (1,3)	f(x)=4x^2-x^3 , (1,3)	$f (x) = 4 x^{2} - x^{3}$ , $(1, 3)$
86173	Find the Tangent Line at (1,0)	(x^2-1)/(x^2+x+1) , (1,0)	$\frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
86174	Find the Tangent Line at x=2	f(x)=(10x-4)^(1/2) , x=2	$f (x) = {(10 x - 4)}^{\frac{1}{2}}$ , $x = 2$
86175	Find the Tangent Line at (3,-18)	f(x)=(1-x)(x^2-6)^2 ; (3,-18)	$f (x) = (1 - x) {(x^{2} - 6)}^{2}$ ; $(3, - 18)$
86176	Find the Tangent Line at (4,36)	y=x^2+5x , (4,36)	$y = x^{2} + 5 x$ , $(4, 36)$
86177	Find the Tangent Line at (2,3)	x^2+xy-y^2=1 , (2,3)	$x^{2} + x y - y^{2} = 1$ , $(2, 3)$
86178	Find the Tangent Line at (2,2)	x^4+5y^2=36 , (2,2)	$x^{4} + 5 y^{2} = 36$ , $(2, 2)$
86179	Find the Tangent Line at (-1,11)	f(x)=2x^2-4x+5 at the point (-1,11)	$f (x) = 2 x^{2} - 4 x + 5$ at the point $(- 1, 11)$
86180	Find the Tangent Line at (1,1)	y = square root of x , (1,1)	$y = \sqrt{x}$ , $(1, 1)$
86181	Find the Tangent Line at (49,7)	f(x) = square root of x , (49,7)	$f (x) = \sqrt{x}$ , $(49, 7)$
86182	Find the Tangent Line at (2,-16)	y=-2x^3 , (2,-16)	$y = - 2 x^{3}$ , $(2, - 16)$
86183	Find the Tangent Line at (0,1)	y=sin(x)+cos(x) , (0,1)	$y = \sin (x) + \cos (x)$ , $(0, 1)$
86184	Find the Tangent Line at (1,3)	x^2+y^2=10 , (1,3)	$x^{2} + y^{2} = 10$ , $(1, 3)$
86185	Find the Tangent Line at (-2,-16)	y=2x^3 , (-2,-16)	$y = 2 x^{3}$ , $(- 2, - 16)$
86186	Find the Tangent Line at (0,1)	y=5^x , (0,1)	$y = 5^{x}$ , $(0, 1)$
86187	Find the Tangent Line at (0,8)	y=8e^x+x , (0,8)	$y = 8 e^{x} + x$ , $(0, 8)$
86188	Find the Tangent Line at x=π/3	y=2sin(x)cos(x) ; x=pi/3	$y = 2 \sin (x) \cos (x)$ ; $x = \frac{π}{3}$
86189	Find the Tangent Line at (0,1/5)	y=(1+x)/(4+e^x) , (0,1/5)	$y = \frac{1 + x}{4 + e^{x}}$ , $(0, \frac{1}{5})$
86190	Find the Tangent Line at (25,5)	f(x) = square root of x , (25,5)	$f (x) = \sqrt{x}$ , $(25, 5)$
86191	Find the Tangent Line at (25,26/5)	f(x) = square root of x+1/( square root of x) ; (25,26/5)	$f (x) = \sqrt{x} + \frac{1}{\sqrt{x}}$ ; $(25, \frac{26}{5})$
86192	Find the Tangent Line at (3,3)	y=(4x)/(x+1) , (3,3)	$y = \frac{4 x}{x + 1}$ , $(3, 3)$
86193	Find the Tangent Line at (81,9)	f(x) = square root of x , (81,9)	$f (x) = \sqrt{x}$ , $(81, 9)$
86194	Find the Tangent Line at (2,16)	y=2x^3 , (2,16)	$y = 2 x^{3}$ , $(2, 16)$
86195	Find the Tangent Line at (1,4)	y=4 square root of x , (1,4)	$y = 4 \sqrt{x}$ , $(1, 4)$
86196	Find the Tangent Line at x=4	f(x)=(4x-7)^(1/2) , x=4	$f (x) = {(4 x - 7)}^{\frac{1}{2}}$ , $x = 4$
86197	Find the Tangent Line at (1,3)	y=x^4+3x^2-x , (1,3)	$y = x^{4} + 3 x^{2} - x$ , $(1, 3)$
86198	Find the Tangent Line at (3,23)	y=x^3-2x+2 , (3,23)	$y = x^{3} - 2 x + 2$ , $(3, 23)$
86199	Find the Tangent Line at x=π/4	y=4sin(x)cos(x) ; x=pi/4	$y = 4 \sin (x) \cos (x)$ ; $x = \frac{π}{4}$
86200	Find the Tangent Line at x=-1	f(x)=-x^2+4x+2 at x=-1	$f (x) = - x^{2} + 4 x + 2$ at $x = - 1$