Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
52601	Find the Tangent Line at the Point	f(x)=2x^3 , (-2,-16)	$f (x) = 2 x^{3}$ , $(- 2, - 16)$
52602	Solve by Addition/Elimination	-x+3y=0 -6x-y=0	$- x + 3 y = 0$ $- 6 x - y = 0$
52603	Find the Tangent Line at the Point	y = square root of x , (64,8)	$y = \sqrt{x}$ , $(64, 8)$
52604	Find the Tangent Line at the Point	y=6sin(pix-y) , (-1,0)	$y = 6 \sin (π x - y)$ , $(- 1, 0)$
52605	Find the Tangent Line at the Point	xcos(y)=1 , (2,pi/3)	$x \cos (y) = 1$ , $(2, \frac{π}{3})$
52606	Find the Tangent Line at the Point	h(t)=-2t^3 , (-1,2)	$h (t) = - 2 t^{3}$ , $(- 1, 2)$
52607	Find the Tangent Line at the Point	y=4sin(pix-y) , (1,0)	$y = 4 \sin (π x - y)$ , $(1, 0)$
52608	Find the Tangent Line at the Point	y=(3x-1)^-6 , (0,1)	$y = {(3 x - 1)}^{- 6}$ , $(0, 1)$
52609	Find the Tangent Line at the Point	f(x)=tan(x) , (-pi/4,-1)	$f (x) = \tan (x)$ , $(- \frac{π}{4}, - 1)$
52610	Find the Tangent Line at the Point	f(x)=tan(x)^2 , (-pi/4,1)	$f (x) = \tan^{2} (x)$ , $(- \frac{π}{4}, 1)$
52611	Find the Tangent Line at the Point	x^2+2xy-y^2+x=74 , (6,8)	$x^{2} + 2 x y - y^{2} + x = 74$ , $(6, 8)$
52612	Find the Tangent Line at the Point	cos(5y)=x ; (0,pi/10)	$\cos (5 y) = x$ ; $(0, \frac{π}{10})$
52613	Find the Tangent Line at the Point	f(x)=tan(x)^2 , (pi/4,1)	$f (x) = \tan^{2} (x)$ , $(\frac{π}{4}, 1)$
52614	Find the Tangent Line at the Point	x^2+y^2=(4x^2+4y^2-x)^2 , (0,0.25)	$x^{2} + y^{2} = {(4 x^{2} + 4 y^{2} - x)}^{2}$ , $(0, 0.25)$
52615	Find the Tangent Line at the Point	x^2+y^2=64 (0,-8)	$x^{2} + y^{2} = 64$ $(0, - 8)$
52616	Find the Tangent Line at the Point	x^2y^2=9 , (-1,3)	$x^{2} y^{2} = 9$ , $(- 1, 3)$
52617	Find the Tangent Line at the Point	x^2-y^2=36 , (6,0)	$x^{2} - y^{2} = 36$ , $(6, 0)$
52618	Find the Tangent Line at the Point	y=7x-x^3 , (1,6)	$y = 7 x - x^{3}$ , $(1, 6)$
52619	Find the Tangent Line at the Point	x^2+y^2=50 , (5,-5)	$x^{2} + y^{2} = 50$ , $(5, - 5)$
52620	Find the Tangent Line at the Point	g(x)=x^2-8 , (2,-4)	$g (x) = x^{2} - 8$ , $(2, - 4)$
52621	Find the Tangent Line at the Point	arctan(x+y)=y^2+pi/4 , (1,0)	$\arctan (x + y) = y^{2} + \frac{π}{4}$ , $(1, 0)$
52622	Find the Tangent Line at the Point	xy-3y^2=2 , (7,2)	$x y - 3 y^{2} = 2$ , $(7, 2)$
52623	Find the Tangent Line at the Point	f(x)=x^2+6 , (5,31)	$f (x) = x^{2} + 6$ , $(5, 31)$
52624	Find the Tangent Line at the Point	sec(x) , (pi/3,2)	$\sec (x)$ , $(\frac{π}{3}, 2)$
52625	Find the Tangent Line at the Point	y=14xsin(x) , (pi/2,7pi)	$y = 14 x \sin (x)$ , $(\frac{π}{2}, 7 π)$
52626	Find the Tangent Line at the Point	5e^x+x , (0,5)	$5 e^{x} + x$ , $(0, 5)$
52627	Find the Tangent Line at the Point	cos(3y)=x ; (0,pi/6)	$\cos (3 y) = x$ ; $(0, \frac{π}{6})$
52628	Find the Tangent Line at the Point	y=-1/(x^3) , (-2,1/8)	$y = - \frac{1}{x^{3}}$ , $(- 2, \frac{1}{8})$
52629	Find the Tangent Line at the Point	g(x)=x^2-11 , (3,-2)	$g (x) = x^{2} - 11$ , $(3, - 2)$
52630	Find the Tangent Line at the Point	y=arcsec(6x) , (( square root of 2)/6,pi/4)	$y = arcsec (6 x)$ , $(\frac{\sqrt{2}}{6}, \frac{π}{4})$
52631	Find the Tangent Line at the Point	y^2=125x ; (5,25)	$y^{2} = 125 x$ ; $(5, 25)$
52632	Find the Tangent Line at the Point	y^4-4y^2=x^4-9x^2 , (-3,-2)	$y^{4} - 4 y^{2} = x^{4} - 9 x^{2}$ , $(- 3, - 2)$
52633	Find the Tangent Line at the Point	f(x)=(x^3+4)(3x^2-4x+2) ; (1,5)	$f (x) = (x^{3} + 4) (3 x^{2} - 4 x + 2)$ ; $(1, 5)$
52634	Find the Tangent Line at the Point	y=3sin(pix-y) , (1,0)	$y = 3 \sin (π x - y)$ , $(1, 0)$
52635	Find the Tangent Line at the Point	18(x^2+y^2)^2=169xy^2 , (2,3)	$18 {(x^{2} + y^{2})}^{2} = 169 x y^{2}$ , $(2, 3)$
52636	Find the Tangent Line at the Point	x^2+3y^2=13 ; (1,2)	$x^{2} + 3 y^{2} = 13$ ; $(1, 2)$
52637	Find the Tangent Line at the Point	y=7+cot(x)-2csc(x) , (pi/2,5)	$y = 7 + \cot (x) - 2 \csc (x)$ , $(\frac{π}{2}, 5)$
52638	Find the Tangent Line at the Point	y=arctan(1/5x) ; (5,pi/4)	$y = \arctan (\frac{1}{5} x)$ ; $(5, \frac{π}{4})$
52639	Find the Tangent Line at the Point	y=1/3arctan(1/4x) , (4,pi/12)	$y = \frac{1}{3} \arctan (\frac{1}{4} x)$ , $(4, \frac{π}{12})$
52640	Find the Tangent Line at the Point	y=x square root of x , (9,27)	$y = x \sqrt{x}$ , $(9, 27)$
52641	Find the Tangent Line at the Point	3(x^2+y^2)^2=100xy^2 ; (3,1)	$3 {(x^{2} + y^{2})}^{2} = 100 x y^{2}$ ; $(3, 1)$
52642	Find the Tangent Line at the Point	y=( square root of x)/(x+3) , (4,2/7)	$y = \frac{\sqrt{x}}{x + 3}$ , $(4, \frac{2}{7})$
52643	Find the Tangent Line at the Point	y = square root of x ; (81,9)	$y = \sqrt{x}$ ; $(81, 9)$
52644	Find the Tangent Line at the Point	y=9x-x^2 , (1,8)	$y = 9 x - x^{2}$ , $(1, 8)$
52645	Find the Tangent Line at the Point	x^2+xy-y^2=44 ; (6,2)	$x^{2} + x y - y^{2} = 44$ ; $(6, 2)$
52646	Find the Tangent Line at the Point	y=6sin(pix+y) , (-1,0)	$y = 6 \sin (π x + y)$ , $(- 1, 0)$
52647	Find the Tangent Line at the Point	y=e^(3x) , (0,1)	$y = e^{3 x}$ , $(0, 1)$
52648	Find the Tangent Line at the Point	f(x)=-5/3x^2+2x+2 ; (-1,-5/3)	$f (x) = - \frac{5}{3} x^{2} + 2 x + 2$ ; $(- 1, - \frac{5}{3})$
52649	Find the Tangent Line at the Point	x^3+y^3=16xy ; (8,8)	$x^{3} + y^{3} = 16 x y$ ; $(8, 8)$
52650	Find the Tangent Line at the Point	x^2y^2=36 (-3,2)	$x^{2} y^{2} = 36$ $(- 3, 2)$
52651	Find the Tangent Line at the Point	y=3x^3-x^2+9 , (2,29)	$y = 3 x^{3} - x^{2} + 9$ , $(2, 29)$
52652	Find the Tangent Line at the Point	48(x^2+y^2)=625xy^2 ; (3,4)	$48 (x^{2} + y^{2}) = 625 x y^{2}$ ; $(3, 4)$
52653	Find the Tangent Line at the Point	g(x)=13-x^2 ; (3,4)	$g (x) = 13 - x^{2}$ ; $(3, 4)$
52654	Find the Tangent Line at the Point	x^2+y^2=29 , (5,2)	$x^{2} + y^{2} = 29$ , $(5, 2)$
52655	Find the Tangent Line at the Point	f(x)=-6sin(x) , (0,pi/2)	$f (x) = - 6 \sin (x)$ , $(0, \frac{π}{2})$
52656	Find the Tangent Line at the Point	y=5sin(pix+y) , (1,0)	$y = 5 \sin (π x + y)$ , $(1, 0)$
52657	Find the Tangent Line at the Point	g(x)=(7x)/(x-3) , (6,14)	$g (x) = \frac{7 x}{x - 3}$ , $(6, 14)$
52658	Determine if True	tan(pi/2)=infinity	$\tan (\frac{π}{2}) = \infty$
52659	Find the Inflection Points	f(x)=4x^3+12x^2-96x+8	$f (x) = 4 x^{3} + 12 x^{2} - 96 x + 8$
52660	Find the Inflection Points	f(x)=5sin(x)+sin(2x)	$f (x) = 5 \sin (x) + \sin (2 x)$
52661	Find the Inflection Points	f(x)=4x^6-7x^5	$f (x) = 4 x^{6} - 7 x^{5}$
52662	Find the Inflection Points	f(x)=-4x^3-8x^2+32	$f (x) = - 4 x^{3} - 8 x^{2} + 32$
52663	Find the Inflection Points	f(x)=7-4x^4	$f (x) = 7 - 4 x^{4}$
52664	Find the Inflection Points	f(x)=-5-x^(4/5)	$f (x) = - 5 - x^{\frac{4}{5}}$
52665	Find the Inflection Points	f(x)=5x^3-30x^2-6x-2	$f (x) = 5 x^{3} - 30 x^{2} - 6 x - 2$
52666	Find the Inflection Points	f(x)=3x^4-3x^3+5	$f (x) = 3 x^{4} - 3 x^{3} + 5$
52667	Find the Inflection Points	f(x)=x^3+6x^2+12x-8	$f (x) = x^{3} + 6 x^{2} + 12 x - 8$
52668	Find the Inflection Points	f(x)=x^3+4x^2-21x	$f (x) = x^{3} + 4 x^{2} - 21 x$
52669	Find the Inflection Points	f(x)=-x^3-12x^2-48x+1	$f (x) = - x^{3} - 12 x^{2} - 48 x + 1$
52670	Find the Inflection Points	f(x)=-x^3+9x^2-27x+8	$f (x) = - x^{3} + 9 x^{2} - 27 x + 8$
52671	Find the Inflection Points	f(x)=-x^3+9x^2-24x-4	$f (x) = - x^{3} + 9 x^{2} - 24 x - 4$
52672	Find the Inflection Points	f(x)=9-7x^4	$f (x) = 9 - 7 x^{4}$
52673	Find the Inflection Points	f(x)=-7x^3+21x+8	$f (x) = - 7 x^{3} + 21 x + 8$
52674	Find the Inflection Points	f(x)=x^2(2-5x)^3	$f (x) = x^{2} {(2 - 5 x)}^{3}$
52675	Find the Inflection Points	f(x)=x^2e^(18x)	$f (x) = x^{2} e^{18 x}$
52676	Find the Inflection Points	f(x)=x^3+15x^2+75x-4	$f (x) = x^{3} + 15 x^{2} + 75 x - 4$
52677	Find the Inflection Points	g(x)=4x^3-9x	$g (x) = 4 x^{3} - 9 x$
52678	Find the Inflection Points	g(x)=4x^4-8x^3+10	$g (x) = 4 x^{4} - 8 x^{3} + 10$
52679	Find the Inflection Points	g(x)=3x^4-6x^3+8	$g (x) = 3 x^{4} - 6 x^{3} + 8$
52680	Find the Inflection Points	f(x)=-x^6+18x^5-18x+5	$f (x) = - x^{6} + 18 x^{5} - 18 x + 5$
52681	Find the Inflection Points	f(x)=x^7 natural log of x	$f (x) = x^{7} \ln (x)$
52682	Find the Inflection Points	f(x)=x^3-6x^2+26x-36	$f (x) = x^{3} - 6 x^{2} + 26 x - 36$
52683	Find the Inflection Points	f(x)=x^3-8x^2-12x+2	$f (x) = x^{3} - 8 x^{2} - 12 x + 2$
52684	Find the Inflection Points	f(x)=x^3-3x^2-9x+9	$f (x) = x^{3} - 3 x^{2} - 9 x + 9$
52685	Find the Inflection Points	f(x)=x^3-3x^2+28x-26	$f (x) = x^{3} - 3 x^{2} + 28 x - 26$
52686	Find the Inflection Points	f(x)=x^3-3x^2+29x-27	$f (x) = x^{3} - 3 x^{2} + 29 x - 27$
52687	Find the Inflection Points	f(x)=x^3-27x+9	$f (x) = x^{3} - 27 x + 9$
52688	Find the Inflection Points	f(x)=x^4-18x^2+5	$f (x) = x^{4} - 18 x^{2} + 5$
52689	Find the Inflection Points	f(x)=1/3e^(-x)	$f (x) = \frac{1}{3} e^{- x}$
52690	Find the Inflection Points	f(x)=(2x)/(x^2-25)	$f (x) = \frac{2 x}{x^{2} - 25}$
52691	Find the Inflection Points	f(x)=-5/(x-6)	$f (x) = \frac{- 5}{x - 6}$
52692	Find the Inflection Points	f(x)=230+8x^3+x^4	$f (x) = 230 + 8 x^{3} + x^{4}$
52693	Find the Inflection Points	f(x)=(x+1)^3(x+2)^2	$f (x) = {(x + 1)}^{3} {(x + 2)}^{2}$
52694	Find the Inflection Points	f(x)=x/( natural log of x)	$f (x) = \frac{x}{\ln (x)}$
52695	Find the Inflection Points	f(x)=(6-x)e^(-x)	$f (x) = (6 - x) e^{- x}$
52696	Find the Inflection Points	f(x)=17+12x^2-2x^3	$f (x) = 17 + 12 x^{2} - 2 x^{3}$
52697	Use the Rational Roots Test to Find All Possible Roots	p(x)=35x^4+24x^3+17x^2-5x-10	$p (x) = 35 x^{4} + 24 x^{3} + 17 x^{2} - 5 x - 10$
52698	Use the Rational Roots Test to Find All Possible Roots	f(x)=11x^3+126x^2+56x+11	$f (x) = 11 x^{3} + 126 x^{2} + 56 x + 11$
52699	Find the Equation with a Point and y-intercept	(x+2)^2+(y-3)^2=37 , (-8,2)	${(x + 2)}^{2} + {(y - 3)}^{2} = 37$ , $(- 8, 2)$
52700	Find the Equation with a Point and y-intercept	y=(e^x)/x , (1,e)	$y = \frac{e^{x}}{x}$ , $(1, e)$