Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
24901	Find the Horizontal Tangent Line	y=x^3-4x	$y = x^{3} - 4 x$
24902	Find the Horizontal Tangent Line	y=x^3-3x^2	$y = x^{3} - 3 x^{2}$
24903	Find the Horizontal Tangent Line	y=x^3-5x^2+3x+1	$y = x^{3} - 5 x^{2} + 3 x + 1$
24904	Find the Horizontal Tangent Line	y=x^3-3x	$y = x^{3} - 3 x$
24905	Find the Horizontal Tangent Line	y=x^3-3x+1	$y = x^{3} - 3 x + 1$
24906	Find the Horizontal Tangent Line	y=5^x	$y = 5^{x}$
24907	Find the Horizontal Tangent Line	y = fourth root of x	$y = \sqrt[4]{x}$
24908	Find the Horizontal Tangent Line	y=x/(x-3)	$y = \frac{x}{x - 3}$
24909	Find the Horizontal Tangent Line	y = square root of x	$y = \sqrt{x}$
24910	Find the Horizontal Tangent Line	y=1/2x^2+7x	$y = \frac{1}{2} x^{2} + 7 x$
24911	Find the Horizontal Tangent Line	y=1/3x^3-2x+7	$y = \frac{1}{3} x^{3} - 2 x + 7$
24912	Find the Horizontal Tangent Line	y=1/x	$y = \frac{1}{x}$
24913	Find the Horizontal Tangent Line	sin(2x)	$\sin (2 x)$
24914	Graph	(192x)/((x^2+16)^2)=0	$\frac{192 x}{{(x^{2} + 16)}^{2}} = 0$
24915	Graph	(4(x-6))/(x^4)=0	$\frac{4 (x - 6)}{x^{4}} = 0$
24916	Graph	((2x-1)(x+2))/((x+1)(x-2))	$\frac{(2 x - 1) (x + 2)}{(x + 1) (x - 2)}$
24917	Solve Using the Square Root Property	f(2)=3/2	$f (2) = \frac{3}{2}$
24918	Write as an Equation	f(x)=2x-1	$f (x) = 2 x - 1$
24919	Graph	(x-2)(x+7)=0	$(x - 2) (x + 7) = 0$
24920	Graph	(y)=1/3*(x-1)	$(y) = \frac{1}{3} \cdot (x - 1)$
24921	Graph	(\|x\|)/(x+1)	$\frac{\| x \|}{x + 1}$
24922	Graph	((x-2)^2)/9-((y-3)^2)/4=1	$\frac{{(x - 2)}^{2}}{9} - \frac{{(y - 3)}^{2}}{4} = 1$
24923	Find Where Increasing/Decreasing Using Derivatives	f(x)=1-x^(1/3)	$f (x) = 1 - x^{\frac{1}{3}}$
24924	Graph	((x-2)^2)/25-((y+3)^2)/4=1	$\frac{{(x - 2)}^{2}}{25} - \frac{{(y + 3)}^{2}}{4} = 1$
24925	Graph	((y-7)^2)/36-((x-4)^2)/64=1	$\frac{{(y - 7)}^{2}}{36} - \frac{{(x - 4)}^{2}}{64} = 1$
24926	Graph	0.80x+75	$0.8 x + 75$
24927	Graph	(x-4)^2+(y-2)^2=25	${(x - 4)}^{2} + {(y - 2)}^{2} = 25$
24928	Find the Linearization at x=6	f(x)=x+7 , x=6	$f (x) = x + 7$ , $x = 6$
24929	Find the Linearization at a=0	f(x)=sin(x) , a=0	$f (x) = \sin (x)$ , $a = 0$
24930	Find the Linearization at a=2	f(x) = square root of x^2+21 , a=2	$f (x) = \sqrt{x^{2} + 21}$ , $a = 2$
24931	Graph	(5/2,7/2) , (9/2,1/2) , (3/2,5/2) , (-1/2,11/2)	$(\frac{5}{2}, \frac{7}{2}) (\frac{9}{2}, \frac{1}{2}) (\frac{3}{2}, \frac{5}{2}) (- \frac{1}{2}, \frac{11}{2})$
24932	Determine if Odd, Even, or Neither	f(x)=1+3x^3-x^5	$f (x) = 1 + 3 x^{3} - x^{5}$
24933	Determine if Odd, Even, or Neither	f(x)=(x^2-3)*e^x	$f (x) = (x^{2} - 3) \cdot e^{x}$
24934	Determine if Odd, Even, or Neither	f(x)=sin(17x^2+3x+3)	$f (x) = \sin (17 x^{2} + 3 x + 3)$
24935	Determine if Odd, Even, or Neither	f(x)=3	$f (x) = 3$
24936	Determine if Odd, Even, or Neither	f(x)=-5x^5-3x^3	$f (x) = - 5 x^{5} - 3 x^{3}$
24937	Find the Average Rate of Change	y=4x^2+3 , (1,7) , (1.1,7.84)	$y = 4 x^{2} + 3$ , $(1, 7)$ , $(1.1, 7.84)$
24938	Determine if Odd, Even, or Neither	f(x)=x\|x\|	$f (x) = x \| x \|$
24939	Evaluate	15(20)^2-1/2*(20)^3	$15 {(20)}^{2} - \frac{1}{2} \cdot {(20)}^{3}$
24940	Find the Linearization at a	f(x)=12x^2+8x , x=9	$f (x) = 12 x^{2} + 8 x$ , $x = 9$
24941	Find the Linearization at a=1	f(x)=x^4+3x^2 , a=1	$f (x) = x^{4} + 3 x^{2}$ , $a = 1$
24942	Find the Linearization at a=-1	f(x)=x^4+5x^2 , a=-1	$f (x) = x^{4} + 5 x^{2}$ , $a = - 1$
24943	Write as an Equation	f(x)=3x^3-5	$f (x) = 3 x^{3} - 5$
24944	Write as an Equation	f(x)=((6.001)^2-6*6.001)/((6.001)^2-(6.001)-30)	$f (x) = \frac{{(6.001)}^{2} - 6 \cdot 6.001}{{(6.001)}^{2} - (6.001) - 30}$
24945	Find Where dy/dx is Equal to Zero	y=9x-3x^2+x^3	$y = 9 x - 3 x^{2} + x^{3}$
24946	Find Where dy/dx is Equal to Zero	y=6-x^2	$y = 6 - x^{2}$
24947	Find Where dy/dx is Equal to Zero	y=6x-4cos(3x)	$y = 6 x - 4 \cos (3 x)$
24948	Find Where dy/dx is Equal to Zero	y=x^2+7.5x+4	$y = x^{2} + 7.5 x + 4$
24949	Find Where dy/dx is Equal to Zero	y=12x^3-27x^2-36x+8	$y = 12 x^{3} - 27 x^{2} - 36 x + 8$
24950	Find Where dy/dx is Equal to Zero	xy=4	$x y = 4$
24951	Find Where dy/dx is Equal to Zero	y=2x^2+5	$y = 2 x^{2} + 5$
24952	Find Where dy/dx is Equal to Zero	y=2+48x^2+32x^4	$y = 2 + 48 x^{2} + 32 x^{4}$
24953	Find Where dy/dx is Equal to Zero	xy=1	$x y = 1$
24954	Find Where dy/dx is Equal to Zero	y=(4(x)^3)/((x-1)^2)	$y = \frac{4 {(x)}^{3}}{{(x - 1)}^{2}}$
24955	Find Where dy/dx is Equal to Zero	y=\|x^2-9\|	$y = \| x^{2} - 9 \|$
24956	Find Where dy/dx is Equal to Zero	x+tan(xy)=0	$x + \tan (x y) = 0$
24957	Find Where dy/dx is Equal to Zero	x=cos(y)	$x = \cos (y)$
24958	Find Where dy/dx is Equal to Zero	x natural log of y+y^6=9 natural log of x	$x \ln (y) + y^{6} = 9 \ln (x)$
24959	Find Where dy/dx is Equal to Zero	y+cos(y)=x+1	$y + \cos (y) = x + 1$
24960	Find Where dy/dx is Equal to Zero	5x^2-2xy+7y^2=0	$5 x^{2} - 2 x y + 7 y^{2} = 0$
24961	Find Where dy/dx is Equal to Zero	9x^2+25y^2=225	$9 x^{2} + 25 y^{2} = 225$
24962	Evaluate the Function	f(x)=( natural log of x)^3 at x=6	$9 \cos (x) \sin (y) = 2$
24963	Find Where dy/dx is Equal to Zero	tan(4x+y)=4x	$\tan (4 x + y) = 4 x$
24964	Find Where dy/dx is Equal to Zero	cot(y)=x-y	$\cot (y) = x - y$
24965	Find Where dy/dx is Equal to Zero	4y^3+xy-y=500x^4	$4 y^{3} + x y - y = 500 x^{4}$
24966	Find Where dy/dx is Equal to Zero	4x+9y=7	$4 x + 9 y = 7$
24967	Find Where dy/dx is Equal to Zero	5x^3=-3xy+2	$5 x^{3} = - 3 x y + 2$
24968	Find Where dy/dx is Equal to Zero	3xy = natural log of x	$3 x y = \ln (x)$
24969	Find Where dy/dx is Equal to Zero	x^2+xy+y^2=27	$x^{2} + x y + y^{2} = 27$
24970	Find Where dy/dx is Equal to Zero	x^3+y^3=21xy	$x^{3} + y^{3} = 21 x y$
24971	Find Where dy/dx is Equal to Zero	x^3-3x^2y+2xy^2=12	$x^{3} - 3 x^{2} y + 2 x y^{2} = 12$
24972	Find Where dy/dx is Equal to Zero	y^2=x^2+y	$y^{2} = x^{2} + y$
24973	Find Where dy/dx is Equal to Zero	y^2-3xy=2	$y^{2} - 3 x y = 2$
24974	Find Where dy/dx is Equal to Zero	y^4-4y^2=x^4-9x^2	$y^{4} - 4 y^{2} = x^{4} - 9 x^{2}$
24975	Find Where dy/dx is Equal to Zero	10sin(xy)=2x+3y	$10 \sin (x y) = 2 x + 3 y$
24976	Evaluate the Derivative at y=x-2	y=4-x^2 , y=x-2	$y = 4 - x^{2}$ , $y = x - 2$
24977	Find the Critical Points	f(x)=x^4-10x^2	$f (x) = x^{4} - 10 x^{2}$
24978	Find Where dy/dx is Equal to Zero	x^2+y^2=16x	$x^{2} + y^{2} = 16 x$
24979	Find the Absolute Max and Min over the Interval	f(x)=x+9/x , [3,20]	$f (x) = x + \frac{9}{x}$ , $[3, 20]$
24980	Find the Absolute Max and Min over the Interval	f(x)=x+e^(-4x) , [-2,3]	$f (x) = x + e^{- 4 x}$ , $[- 2, 3]$
24981	Find the Absolute Max and Min over the Interval	g(x)=2x^2-x-1 , [3,5]	$g (x) = 2 x^{2} - x - 1$ , $[3, 5]$
24982	Find the Absolute Max and Min over the Interval	f(x)=18x^2-3/2x^3 , [0,12]	$f (x) = 18 x^{2} - \frac{3}{2} x^{3}$ , $[0, 12]$
24983	Find the Absolute Max and Min over the Interval	f(x)=4x^3-6x^2-144x+9 , [-4,5]	$f (x) = 4 x^{3} - 6 x^{2} - 144 x + 9$ , $[- 4, 5]$
24984	Find the Absolute Max and Min over the Interval	f(x)=3+5x-5x^2 , [0,4]	$f (x) = 3 + 5 x - 5 x^{2}$ , $[0, 4]$
24985	Find the Absolute Max and Min over the Interval	f(x)=8-x , (-3,5)	$f (x) = 8 - x$ , $(- 3, 5)$
24986	Find the Absolute Max and Min over the Interval	f(x)=9x^2-3/2x^3 , [0,6]	$f (x) = 9 x^{2} - \frac{3}{2} x^{3}$ , $[0, 6]$
24987	Find the Absolute Max and Min over the Interval	f(x)=x+1/x , [1,5]	$f (x) = x + \frac{1}{x}$ , $[1, 5]$
24988	Find the Absolute Max and Min over the Interval	f(x)=(x^2-36)/(x^2+36) , [-36,36]	$f (x) = \frac{x^{2} - 36}{x^{2} + 36}$ , $[- 36, 36]$
24989	Find the Absolute Max and Min over the Interval	f(x)=9/(x-1) , [1,4]	$f (x) = \frac{9}{x - 1}$ , $[1, 4]$
24990	Find the Absolute Max and Min over the Interval	f(x)=x^4-8x^2-1 , [-3,4]	$f (x) = x^{4} - 8 x^{2} - 1$ , $[- 3, 4]$
24991	Find the Absolute Max and Min over the Interval	f(x)=x^3-9x^2+24x-14 , [-2,3]	$f (x) = x^{3} - 9 x^{2} + 24 x - 14$ , $[- 2, 3]$
24992	Find the Absolute Max and Min over the Interval	f(x)=2x^3+3x^2-36x+7 , (-3,6)	$f (x) = 2 x^{3} + 3 x^{2} - 36 x + 7$ , $(- 3, 6)$
24993	Find the Absolute Max and Min over the Interval	f(x)=x^3-12x , [0,4]	$f (x) = x^{3} - 12 x$ , $[0, 4]$
24994	Find the Absolute Max and Min over the Interval	f(x)=x^3-2x^2-15x+10 , [-2,0]	$f (x) = x^{3} - 2 x^{2} - 15 x + 10$ , $[- 2, 0]$
24995	Find the Absolute Max and Min over the Interval	f(x)=x^2+x-4 , [0,8]	$f (x) = x^{2} + x - 4$ , $[0, 8]$
24996	Find the Absolute Max and Min over the Interval	f(x)=x^2-2x+6 , (0,3)	$f (x) = x^{2} - 2 x + 6$ , $(0, 3)$
24997	Find the Absolute Max and Min over the Interval	f(x)=x^3-x^2-8x+8 , [-2,0]	$f (x) = x^{3} - x^{2} - 8 x + 8$ , $[- 2, 0]$
24998	Find the Absolute Max and Min over the Interval	f(x)=(4x)/(x^2+9) , [-4,4]	$f (x) = \frac{4 x}{x^{2} + 9}$ , $[- 4, 4]$
24999	Find the Absolute Max and Min over the Interval	f(x)=x^(7/3)+x^(4/3)-3x^(1/3) , [-1,3]	$f (x) = x^{\frac{7}{3}} + x^{\frac{4}{3}} - 3 x^{\frac{1}{3}}$ , $[- 1, 3]$
25000	Find the Absolute Max and Min over the Interval	f(x)=x/(x^2-x+1) , [0,3]	$f (x) = \frac{x}{x^{2} - x + 1}$ , $[0, 3]$