Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
60701	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-9x^2-81x	$f (x) = x^{3} - 9 x^{2} - 81 x$
60702	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-27x	$f (x) = x^{3} - 27 x$
60703	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^5-5x^4-x^3+28x^2-2x	$f (x) = x^{5} - 5 x^{4} - x^{3} + 28 x^{2} - 2 x$
60704	Find Where Increasing/Decreasing Using Derivatives	f(x)=x+2cos(x)	$f (x) = x + 2 \cos (x)$
60705	Find Where Increasing/Decreasing Using Derivatives	f(x)=x natural log of x	$f (x) = x \ln (x)$
60706	Find the Inverse	f(x) = square root of 2x-1	$f (x) = \sqrt{2 x - 1}$
60707	Find Where Increasing/Decreasing Using Derivatives	f(x)=25-15x^2+5x^3	$f (x) = 25 - 15 x^{2} + 5 x^{3}$
60708	Find Where Increasing/Decreasing Using Derivatives	f(x)=-12x^5+120x^4-300x^3	$f (x) = - 12 x^{5} + 120 x^{4} - 300 x^{3}$
60709	Find Where Increasing/Decreasing Using Derivatives	f(x)=15-9x^2+3x^3	$f (x) = 15 - 9 x^{2} + 3 x^{3}$
60710	Find Where Increasing/Decreasing Using Derivatives	f(x)=10x^6-13x^5	$f (x) = 10 x^{6} - 13 x^{5}$
60711	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^2e^x	$f (x) = x^{2} e^{x}$
60712	Find Where Increasing/Decreasing Using Derivatives	f(x)=6x^6-13x^5	$f (x) = 6 x^{6} - 13 x^{5}$
60713	Find Where Increasing/Decreasing Using Derivatives	f(x)=-6x^5+160x^3	$f (x) = - 6 x^{5} + 160 x^{3}$
60714	Find Where Increasing/Decreasing Using Derivatives	f(x)=5x^(2/3)-2x^(5/3)	$f (x) = 5 x^{\frac{2}{3}} - 2 x^{\frac{5}{3}}$
60715	Find Where Increasing/Decreasing Using Derivatives	f(x)=-2x^4+16x^2+32	$f (x) = - 2 x^{4} + 16 x^{2} + 32$
60716	Find Where Increasing/Decreasing Using Derivatives	f(x)=3cos(x)-cos(x)^3	$f (x) = 3 \cos (x) - \cos^{3} (x)$
60717	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^6-3x^5	$f (x) = 2 x^{6} - 3 x^{5}$
60718	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (3x)/( natural log of x+1)	$lim_{x \to 0} \frac{3 x}{\ln (x + 1)}$
60719	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of (5x^3-2x)/(7x^3+3)	$lim_{x \to \infty} \frac{5 x^{3} - 2 x}{7 x^{3} + 3}$
60720	Evaluate Using L'Hospital's Rule	limit as x approaches 4 of (2x^2+13x+20)/(x+4)	$lim_{x \to 4} \frac{2 x^{2} + 13 x + 20}{x + 4}$
60721	Find the Area Under the Curve	f(x)=9-x^2 ; [0,6]	$f (x) = 9 - x^{2}$ ; $[0, 6]$
60722	Evaluate Using Summation Formulas	sum from k=1 to n of (k^2)/9	$\sum_{k = 1}^{n} \frac{k^{2}}{9}$
60723	Find the Roots (Zeros)	x^3+5x^2-8x-12=0	$x^{3} + 5 x^{2} - 8 x - 12 = 0$
60724	Find the Roots (Zeros)	3x^2-4x-4	$3 x^{2} - 4 x - 4$
60725	Find the Roots (Zeros)	2x-6	$2 x - 6$
60726	Find the Roots (Zeros)	x^2-5x	$x^{2} - 5 x$
60727	Eliminate the Parameter	x=sin(t) , y=3cos(t)	$x = \sin (t)$ , $y = 3 \cos (t)$
60728	Find the Volume	y = square root of 2x+3 , y=0 , x=0 , x=1	$y = \sqrt{2 x + 3}$ , $y = 0$ , $x = 0$ , $x = 1$
60729	Find the Volume	x=y-y^2 , x=0	$x = y - y^{2}$ , $x = 0$
60730	Find the x and y Intercepts	x^3-16x^2+64x	$x^{3} - 16 x^{2} + 64 x$
60731	Find the x and y Intercepts	x^3-12x^2+36x	$x^{3} - 12 x^{2} + 36 x$
60732	Find the Function	f'(x)=-2x square root of 8-x^2	$f' (x) = - 2 x \sqrt{8 - x^{2}}$
60733	Find the Function	f'(x)=8x-9	$f' (x) = 8 x - 9$
60734	Find the Maximum/Minimum Value	f(x)=x+64/x	$f (x) = x + \frac{64}{x}$
60735	Find the Maximum/Minimum Value	f(x)=x^4-2x^2+3	$f (x) = x^{4} - 2 x^{2} + 3$
60736	Find the Maximum/Minimum Value	f(x)=x^3-3x	$f (x) = x^{3} - 3 x$
60737	Find the Maximum/Minimum Value	f(x)=x^2-2x+5	$f (x) = x^{2} - 2 x + 5$
60738	Find dy/dt	y=3t(3t+2)^5	$y = 3 t {(3 t + 2)}^{5}$
60739	Find dx/dy	y=(e^(-x)+1)/(e^x)	$y = \frac{e^{- x} + 1}{e^{x}}$
60740	Find dx/dt	x=10( square root of 1+t^4-1)	$x = 10 (\sqrt{1 + t^{4}} - 1)$
60741	Find dP/dt	P=1/(1+5e^(-1/10t))	$P = \frac{1}{1 + 5 e^{- \frac{1}{10} t}}$
60742	Find the x and y Intercepts	f(x)=(x-4)(x^2-8x-32)	$f (x) = (x - 4) (x^{2} - 8 x - 32)$
60743	Find the x and y Intercepts	f(x)=x^9-9x	$f (x) = x^{9} - 9 x$
60744	Find the Critical Points	f(x)=x/(x^2+16)	$f (x) = \frac{x}{x^{2} + 16}$
60745	Find the Critical Points	f(x)=2x^3+15x^2-36x+90	$f (x) = 2 x^{3} + 15 x^{2} - 36 x + 90$
60746	Find the Critical Points	f(x)=2x^2-3x+1	$f (x) = 2 x^{2} - 3 x + 1$
60747	Find the Critical Points	f(x)=x square root of 9-x^2	$f (x) = x \sqrt{9 - x^{2}}$
60748	Find the Critical Points	f(x)=cos(x)^2	$f (x) = \cos^{2} (x)$
60749	Find the Critical Points	f(x)=x^4-50x^2+625	$f (x) = x^{4} - 50 x^{2} + 625$
60750	Convert to Rectangular Coordinates	(7,135 degrees )	$(7, 135 °)$
60751	Convert to Rectangular Coordinates	(-2,270 degrees )	$(- 2, 270 °)$
60752	Convert to Rectangular Coordinates	(1,150 degrees )	$(1, 150 °)$
60753	Convert to Rectangular Coordinates	(10,225 degrees )	$(10, 225 °)$
60754	Find the Directrix	y=x^2-6x+15	$y = x^{2} - 6 x + 15$
60755	Find the Local Maxima and Minima	2x-2	$2 x - 2$
60756	Find the Local Maxima and Minima	e^(8x)+e^(-x)	$e^{8 x} + e^{- x}$
60757	Find the Local Maxima and Minima	cube root of x	$\sqrt[3]{x}$
60758	Find the Center and Radius	x^2+y^2-20x+8y+115=0	$x^{2} + y^{2} - 20 x + 8 y + 115 = 0$
60759	Find the Center and Radius	x^2+y^2-4x+12y-24=0	$x^{2} + y^{2} - 4 x + 12 y - 24 = 0$
60760	Find the Center and Radius	x^2+y^2-100=0	$x^{2} + y^{2} - 100 = 0$
60761	Find the Center and Radius	x^2+y^2+4x-18y+81=0	$x^{2} + y^{2} + 4 x - 18 y + 81 = 0$
60762	Find the Local Maxima and Minima	x^9+3x^8+2	$x^{9} + 3 x^{8} + 2$
60763	Find the Local Maxima and Minima	x^4-2x^2+1	$x^{4} - 2 x^{2} + 1$
60764	Find the Local Maxima and Minima	(7e^x+7e^(-x))/2	$\frac{7 e^{x} + 7 e^{- x}}{2}$
60765	Find the Local Maxima and Minima	8-x^2-7x-y^2	$8 - x^{2} - 7 x - y^{2}$
60766	Find the Local Maxima and Minima	2x^3-15x^2+36x+1	$2 x^{3} - 15 x^{2} + 36 x + 1$
60767	Find the Local Maxima and Minima	2+3x-x^3	$2 + 3 x - x^{3}$
60768	Find the Local Maxima and Minima	2x^3+x^2-20x+1	$2 x^{3} + x^{2} - 20 x + 1$
60769	Find the Local Maxima and Minima	2x^3+15x^2+24x+7	$2 x^{3} + 15 x^{2} + 24 x + 7$
60770	Find the Directrix	y^2-5y-x+7=0	$y^{2} - 5 y - x + 7 = 0$
60771	Find the Local Maxima and Minima	f(x,y)=x^3-18xy+y^3	$f (x, y) = x^{3} - 18 x y + y^{3}$
60772	Find the Local Maxima and Minima	y=2x^3-24x-2	$y = 2 x^{3} - 24 x - 2$
60773	Find the Local Maxima and Minima	y=2x^3-9x^2+12x	$y = 2 x^{3} - 9 x^{2} + 12 x$
60774	Find the Local Maxima and Minima	f(x,y)=10xy-x^3-5y^2	$f (x, y) = 10 x y - x^{3} - 5 y^{2}$
60775	Find the Maximum/Minimum Value	y=2x^2-4x-5	$y = 2 x^{2} - 4 x - 5$
60776	Find the Maximum/Minimum Value	y=x^2-8x+12	$y = x^{2} - 8 x + 12$
60777	Find the Local Maxima and Minima	f(x,y)=9-x^2-7x-y^2	$f (x, y) = 9 - x^{2} - 7 x - y^{2}$
60778	Find the Local Maxima and Minima	f(x,y)=x^2-2xy+4y^2-6x-6y+8	$f (x, y) = x^{2} - 2 x y + 4 y^{2} - 6 x - 6 y + 8$
60779	Find the Local Maxima and Minima	f(x,y)=x^2-y^2	$f (x, y) = x^{2} - y^{2}$
60780	Find the Local Maxima and Minima	f(x,y)=x^3+y^3-21xy	$f (x, y) = x^{3} + y^{3} - 21 x y$
60781	Find the Local Maxima and Minima	f(x,y)=8xy-x^3-4y^2	$f (x, y) = 8 x y - x^{3} - 4 y^{2}$
60782	Find the Maximum/Minimum Value	f(x,y)=x^2+xy+y^2-3x+2	$f (x, y) = x^{2} + x y + y^{2} - 3 x + 2$
60783	Find the Maximum/Minimum Value	f(x,y)=20xy-x^3-10y^2	$f (x, y) = 20 x y - x^{3} - 10 y^{2}$
60784	Find the Maximum/Minimum Value	f(x,y)=2x^2+4y^2+4x-8y+4	$f (x, y) = 2 x^{2} + 4 y^{2} + 4 x - 8 y + 4$
60785	Find the Inverse	fifth root of x	$\sqrt[5]{x}$
60786	Solve over the Interval	y=e^(2x) ; [0,4]	$y = e^{2 x}$ ; $[0, 4]$
60787	Find the Inflection Points	y=x^3-4x^2-3x+9	$y = x^{3} - 4 x^{2} - 3 x + 9$
60788	Find the Inflection Points	y=2x^3+12x^2+18x	$y = 2 x^{3} + 12 x^{2} + 18 x$
60789	Find the Inflection Points	y=x/(x^2+64)	$y = \frac{x}{x^{2} + 64}$
60790	Find the Inflection Points	y=x^2-6x+5	$y = x^{2} - 6 x + 5$
60791	Find the Inflection Points	f(x)=(x^2)/(x^2-9)	$f (x) = \frac{x^{2}}{x^{2} - 9}$
60792	Find the Inflection Points	f(t)=t+cos(t)	$f (t) = t + \cos (t)$
60793	Find the Inflection Points	f(x)=2xe^x	$f (x) = 2 x e^{x}$
60794	Find the Inflection Points	f(x)=(x-7)(x^2-14x-98)	$f (x) = (x - 7) (x^{2} - 14 x - 98)$
60795	Find the Inflection Points	f(x)=x^4-24x^2	$f (x) = x^{4} - 24 x^{2}$
60796	Find the Inflection Points	f(x)=x^3+3x^2-x-24	$f (x) = x^{3} + 3 x^{2} - x - 24$
60797	Find the Inflection Points	f(x)=x square root of 7-x	$f (x) = x \sqrt{7 - x}$
60798	Convert to Interval Notation	(x-2)(x-5)>40	$(x - 2) (x - 5) > 40$
60799	Solve the System of @WORD	x^2-5x-24<0	$x^{2} - 5 x - 24 < 0$
60800	Convert to Interval Notation	x^2-x-42<=0	$x^{2} - x - 42 \leq 0$