Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
48501	Find the Local Maxima and Minima	1+x-x^2	$1 + x - x^{2}$
48502	Find the Local Maxima and Minima	7cos(2x)+7x	$7 \cos (2 x) + 7 x$
48503	Find the Local Maxima and Minima	64x^2+54/x-3	$64 x^{2} + \frac{54}{x} - 3$
48504	Find the Local Maxima and Minima	x^(4/5)(x+3)	$x^{\frac{4}{5}} (x + 3)$
48505	Find the Local Maxima and Minima	4x+36/x	$4 x + \frac{36}{x}$
48506	Simplify/Condense	natural log of 4- natural log of 1	$\ln (4) - \ln (1)$
48507	Simplify/Condense	cos(arcsin(x))	$\cos (\sin^{-1} (x))$
48508	Find the Inverse	y=( natural log of x)^3	$y = \ln^{3} (x)$
48509	Find the Directrix	y^2=16x	$y^{2} = 16 x$
48510	Find the Directrix	y^2=-36x	$y^{2} = - 36 x$
48511	Find the Inverse	f(x)=e^(2x-4)	$f (x) = e^{2 x - 4}$
48512	Expand Using Sum/Difference Formulas	cos(7/25+8/17)	$\cos (\frac{7}{25} + \frac{8}{17})$
48513	Solve by Graphing	x^5-3x=1	$x^{5} - 3 x = 1$
48514	Evaluate from the Left	limit as x approaches 1 of x/( natural log of x)	$lim_{x \to 1} \frac{x}{\ln (x)}$
48515	Evaluate from the Left	limit as x approaches -pi/2 of sec(x)	$lim_{x \to - \frac{π}{2}} \sec (x)$
48516	Evaluate from the Left	limit as x approaches infinity of arctan(x)	$lim_{x \to \infty} \arctan (x)$
48517	Find Where Increasing/Decreasing Using Derivatives	f(x)=17+12x^2-2x^3	$f (x) = 17 + 12 x^{2} - 2 x^{3}$
48518	Find Where Increasing/Decreasing Using Derivatives	f(x)=-12x^5+105x^4-200x^3	$f (x) = - 12 x^{5} + 105 x^{4} - 200 x^{3}$
48519	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x^2+16)/x	$f (x) = \frac{x^{2} + 16}{x}$
48520	Find Where Increasing/Decreasing Using Derivatives	f(x)=-8x^3+24x+5	$f (x) = - 8 x^{3} + 24 x + 5$
48521	Find Where Increasing/Decreasing Using Derivatives	g(t)=(5t)/(t^2+1)	$g (t) = \frac{5 t}{t^{2} + 1}$
48522	Find Where Increasing/Decreasing Using Derivatives	f(x)=-3x^2+54 natural log of x	$f (x) = - 3 x^{2} + 54 \ln (x)$
48523	Find Where Increasing/Decreasing Using Derivatives	f(x) = square root of 20-x-x^2	$f (x) = \sqrt{20 - x - x^{2}}$
48524	Find Where Increasing/Decreasing Using Derivatives	f(x)=sin(x)^2+sin(x)	$f (x) = \sin^{2} (x) + \sin (x)$
48525	Find Where Increasing/Decreasing Using Derivatives	C(x)=x^(1/3)(x+4)	$C (x) = x^{\frac{1}{3}} (x + 4)$
48526	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^4+4x^3-8x^2+56	$f (x) = x^{4} + 4 x^{3} - 8 x^{2} + 56$
48527	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+12x^2+24x+17	$f (x) = 2 x^{3} + 12 x^{2} + 24 x + 17$
48528	Find Where Increasing/Decreasing Using Derivatives	h(x)=cos((4x)/3)	$h (x) = \cos (\frac{4 x}{3})$
48529	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+6x^2-90x	$f (x) = 2 x^{3} + 6 x^{2} - 90 x$
48530	Find Where Increasing/Decreasing Using Derivatives	f(x)=-5x^3+15x+8	$f (x) = - 5 x^{3} + 15 x + 8$
48531	Find Where Increasing/Decreasing Using Derivatives	f(x)=64x^2+128/x+3	$f (x) = 64 x^{2} + \frac{128}{x} + 3$
48532	Find Where Increasing/Decreasing Using Derivatives	f(x)=-2x^2+16 natural log of x	$f (x) = - 2 x^{2} + 16 \ln (x)$
48533	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-2x^2-4x+7	$f (x) = x^{3} - 2 x^{2} - 4 x + 7$
48534	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+9x^2-60x	$f (x) = 2 x^{3} + 9 x^{2} - 60 x$
48535	Find Where Increasing/Decreasing Using Derivatives	f(t)=0.469t^2+0.758t+0.44	$f (t) = 0.469 t^{2} + 0.758 t + 0.44$
48536	Find Where Increasing/Decreasing Using Derivatives	f(x)=1/3x^3-3/2x^2	$f (x) = \frac{1}{3} x^{3} - \frac{3}{2} x^{2}$
48537	Find Where Increasing/Decreasing Using Derivatives	f(x)=20/(1+9e^(-3x))	$f (x) = \frac{20}{1 + 9 e^{- 3 x}}$
48538	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x^4)/4-2x^3+4x^2	$f (x) = \frac{x^{4}}{4} - 2 x^{3} + 4 x^{2}$
48539	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-48x+3	$f (x) = x^{3} - 48 x + 3$
48540	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^3+18x^2+54x+55	$f (x) = 2 x^{3} + 18 x^{2} + 54 x + 55$
48541	Find the Inverse	f(x)=x^5+3x-2	$f (x) = x^{5} + 3 x - 2$
48542	Find the Inverse	f(x)=-3/4x+6	$f (x) = - \frac{3}{4} x + 6$
48543	Expand Using Sum/Difference Formulas	cos((5pi)/13)	$\cos (\frac{5 π}{13})$
48544	Expand Using Sum/Difference Formulas	sin(225 degrees )	$\sin (225 °)$
48545	Evaluate from the Left	limit as x approaches 2 from the left of 1/(x+2)	$lim_{x \to 2} \frac{1}{x + 2}$
48546	Evaluate from the Left	limit as x approaches 1 of (cos(pix))/(x-1)	$lim_{x \to 1} \frac{\cos (π x)}{x - 1}$
48547	Evaluate from the Left	limit as x approaches 6 of square root of 36-x^2	$lim_{x \to 6} \sqrt{36 - x^{2}}$
48548	Graph the Interval	[-3,3]	$[- 3, 3]$
48549	Find the Vertex	2x^2-10x-1	$2 x^{2} - 10 x - 1$
48550	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^4-20x^3+42x^2-36x	$f (x) = 3 x^{4} - 20 x^{3} + 42 x^{2} - 36 x$
48551	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^(14/15)-x^(29/15)	$f (x) = x^{\frac{14}{15}} - x^{\frac{29}{15}}$
48552	Find Where Increasing/Decreasing Using Derivatives	f(x)=-5x^2+20x	$f (x) = - 5 x^{2} + 20 x$
48553	Find Where Increasing/Decreasing Using Derivatives	f(x)=9-3x+3x^2-x^3	$f (x) = 9 - 3 x + 3 x^{2} - x^{3}$
48554	Find Where Increasing/Decreasing Using Derivatives	f(x)=(3x-8)/x	$f (x) = \frac{3 x - 8}{x}$
48555	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^3-18x^2+36x-27	$f (x) = 3 x^{3} - 18 x^{2} + 36 x - 27$
48556	Find Where Increasing/Decreasing Using Derivatives	f(x)=20x^3-5x^4	$f (x) = 20 x^{3} - 5 x^{4}$
48557	Find Where Increasing/Decreasing Using Derivatives	f(x)=cos((4x)/3)	$f (x) = \cos (\frac{4 x}{3})$
48558	Find Where Increasing/Decreasing Using Derivatives	f(x)=-12x^5+45x^4-40x^3	$f (x) = - 12 x^{5} + 45 x^{4} - 40 x^{3}$
48559	Find Where Increasing/Decreasing Using Derivatives	f(x)=2/3x^3-2x^2-6x-2	$f (x) = \frac{2}{3} x^{3} - 2 x^{2} - 6 x - 2$
48560	Find Where Increasing/Decreasing Using Derivatives	f(x)=75x-x^3	$f (x) = 75 x - x^{3}$
48561	Find Where Increasing/Decreasing Using Derivatives	f(x)=5-27x+9x^2-x^3	$f (x) = 5 - 27 x + 9 x^{2} - x^{3}$
48562	Find Where Increasing/Decreasing Using Derivatives	f(x)=2x^4+3x^3	$f (x) = 2 x^{4} + 3 x^{3}$
48563	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-3x^2-9x+4	$f (x) = x^{3} - 3 x^{2} - 9 x + 4$
48564	Find Where Increasing/Decreasing Using Derivatives	K(t)=(6t)/(t^2+9)	$K (t) = \frac{6 t}{t^{2} + 9}$
48565	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x-4)e^(-3x)	$f (x) = (x - 4) e^{- 3 x}$
48566	Find Where Increasing/Decreasing Using Derivatives	h(x)=12x-x^3	$h (x) = 12 x - x^{3}$
48567	Find Where Increasing/Decreasing Using Derivatives	f(x)=-x^3+9/2x^2+12x-7	$f (x) = - x^{3} + \frac{9}{2} x^{2} + 12 x - 7$
48568	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^(2/11)-x^(3/11)	$f (x) = 3 x^{\frac{2}{11}} - x^{\frac{3}{11}}$
48569	Find Where Increasing/Decreasing Using Derivatives	C(x)=x^(1/5)(x+6)	$C (x) = x^{\frac{1}{5}} (x + 6)$
48570	Find Where Increasing/Decreasing Using Derivatives	f(x)=(9x^2+4)/(9x^2-4)	$f (x) = \frac{(9 x^{2} + 4)}{9 x^{2} - 4}$
48571	Find Where Increasing/Decreasing Using Derivatives	f(x)=-7x^3+21x+9	$f (x) = - 7 x^{3} + 21 x + 9$
48572	Find Where Increasing/Decreasing Using Derivatives	f(x)=x+sin(2x)+5	$f (x) = x + \sin (2 x) + 5$
48573	Find Where Increasing/Decreasing Using Derivatives	f(x)=9x+7x^-1	$f (x) = 9 x + 7 x^{- 1}$
48574	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-5x^2-8x+1	$f (x) = x^{3} - 5 x^{2} - 8 x + 1$
48575	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^(1/9)+9	$f (x) = x^{\frac{1}{9}} + 9$
48576	Find Where Increasing/Decreasing Using Derivatives	f(x) = square root of x^2+9-x	$f (x) = \sqrt{x^{2} + 9} - x$
48577	Find Where Increasing/Decreasing Using Derivatives	f(t)=9/(25-t^2)	$f (t) = \frac{9}{25 - t^{2}}$
48578	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^6-3x^5	$f (x) = x^{6} - 3 x^{5}$
48579	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^(1/3)+1	$f (x) = x^{\frac{1}{3}} + 1$
48580	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^4-18x^2+6	$f (x) = x^{4} - 18 x^{2} + 6$
48581	Find Where Increasing/Decreasing Using Derivatives	f(x)=3x^3-81x+100	$f (x) = 3 x^{3} - 81 x + 100$
48582	Find Where Increasing/Decreasing Using Derivatives	f(x)=-8x+x^2	$f (x) = - 8 x + x^{2}$
48583	Find Where Increasing/Decreasing Using Derivatives	P(x)=-0.005x^2+2x-5000	$P (x) = - 0.005 x^{2} + 2 x - 5000$
48584	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^3-75x+7	$f (x) = x^{3} - 75 x + 7$
48585	Find Where Increasing/Decreasing Using Derivatives	f(x)=15x(x-1)^3	$f (x) = 15 x {(x - 1)}^{3}$
48586	Find Where Increasing/Decreasing Using Derivatives	h(x)=48x-x^3	$h (x) = 48 x - x^{3}$
48587	Find Where Increasing/Decreasing Using Derivatives	f(x)=4x^3-9x^2-12x+9	$f (x) = 4 x^{3} - 9 x^{2} - 12 x + 9$
48588	Find Where Increasing/Decreasing Using Derivatives	f(x)=-12x^5+75x^4-80x^3	$f (x) = - 12 x^{5} + 75 x^{4} - 80 x^{3}$
48589	Find Where Increasing/Decreasing Using Derivatives	f(x)=(x+1)^5-5x-2	$f (x) = {(x + 1)}^{5} - 5 x - 2$
48590	Find Where Increasing/Decreasing Using Derivatives	f(x)=x^2-x- natural log of x	$f (x) = x^{2} - x - \ln (x)$
48591	Find Where Increasing/Decreasing Using Derivatives	f(x)=6x^4+2x^3	$f (x) = 6 x^{4} + 2 x^{3}$
48592	Evaluate from the Left	limit as x approaches 0 of 1/x-1/(\|x\|)	$lim_{x \to 0} \frac{1}{x} - \frac{1}{\| x \|}$
48593	Evaluate from the Left	limit as x approaches 4.75 from the left of arcsin(x/4.75)	$lim_{x \to 4.75} \arcsin (\frac{x}{4.75})$
48594	Find the Vertex	-3x^2+6x-1	$- 3 x^{2} + 6 x - 1$
48595	Find the Vertex	x^2-12x+27	$x^{2} - 12 x + 27$
48596	Find the Vertex	x^2-12x+35	$x^{2} - 12 x + 35$
48597	Find the Inverse	f(x)=(6x-1)/(2x+3)	$f (x) = \frac{6 x - 1}{2 x + 3}$
48598	Find the Inverse	f(x)=e^(2x-3)	$f (x) = e^{2 x - 3}$
48599	Find the Inverse	f(x)=3/x-1	$f (x) = \frac{3}{x} - 1$
48600	Find the Inverse	f(x)=(8x-1)/(2x+3)	$f (x) = \frac{8 x - 1}{2 x + 3}$