Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
50501	Find the Absolute Max and Min over the Interval	f(x)=x-2sin(x) ; [-pi/4,pi/2]	$f (x) = x - 2 \sin (x)$ ; $[- \frac{π}{4}, \frac{π}{2}]$
50502	Find the Absolute Max and Min over the Interval	f(x)=x square root of 25-x^2 , [-1,5]	$f (x) = x \sqrt{25 - x^{2}}$ , $[- 1, 5]$
50503	Find the Absolute Max and Min over the Interval	f(x) = natural log of x^2+5x+9 , [-3,1]	$f (x) = \ln (x^{2} + 5 x + 9)$ , $[- 3, 1]$
50504	Find the Absolute Max and Min over the Interval	f(x)=x^2-6 , [-1,1]	$f (x) = x^{2} - 6$ , $[- 1, 1]$
50505	Find the Absolute Max and Min over the Interval	f(t)=t- cube root of t , [-1,6]	$f (t) = t - \sqrt[3]{t}$ , $[- 1, 6]$
50506	Find the Absolute Max and Min over the Interval	f(x)=1/3(4x+5) , [-9,-2]	$f (x) = \frac{1}{3} (4 x + 5)$ , $[- 9, - 2]$
50507	Find the Absolute Max and Min over the Interval	f(x)=4/3x^3-12x ; [-2,2]	$f (x) = \frac{4}{3} x^{3} - 12 x$ ; $[- 2, 2]$
50508	Find the Absolute Max and Min over the Interval	f(x)=2/3x^3-4x ; [-2,2]	$f (x) = \frac{2}{3} x^{3} - 4 x$ ; $[- 2, 2]$
50509	Find the Absolute Max and Min over the Interval	f(x)=13+2x-x^2 , [0,5]	$f (x) = 13 + 2 x - x^{2}$ , $[0, 5]$
50510	Find the Absolute Max and Min over the Interval	f(x)=27x^2-3/2x^3 ; [0,18]	$f (x) = 27 x^{2} - \frac{3}{2} x^{3}$ ; $[0, 18]$
50511	Find the Absolute Max and Min over the Interval	f(x)=2cos(x)+sin(2x) , [0,pi/2]	$f (x) = 2 \cos (x) + \sin (2 x)$ , $[0, \frac{π}{2}]$
50512	Find the Absolute Max and Min over the Interval	f(x)=3x^4-4x^3 ; [-1,2]	$f (x) = 3 x^{4} - 4 x^{3}$ ; $[- 1, 2]$
50513	Find the Absolute Max and Min over the Interval	f(x)=2x^3-12x^2-72x+2 , [-6,7]	$f (x) = 2 x^{3} - 12 x^{2} - 72 x + 2$ , $[- 6, 7]$
50514	Find the Absolute Max and Min over the Interval	f(x)=2x^3-2x^2-2x+7 ; [-1,0]	$f (x) = 2 x^{3} - 2 x^{2} - 2 x + 7$ ; $[- 1, 0]$
50515	Find the Absolute Max and Min over the Interval	f(x)=2x^3-2x^2-2x+9 ; [-1,2]	$f (x) = 2 x^{3} - 2 x^{2} - 2 x + 9$ ; $[- 1, 2]$
50516	Find the Absolute Max and Min over the Interval	f(x)=2x^3-6x^2-48x+3 , [-3,5]	$f (x) = 2 x^{3} - 6 x^{2} - 48 x + 3$ , $[- 3, 5]$
50517	Find the Absolute Max and Min over the Interval	f(x)=4x^3-6x^2-72x+7 , [-3,4]	$f (x) = 4 x^{3} - 6 x^{2} - 72 x + 7$ , $[- 3, 4]$
50518	Find the Absolute Max and Min over the Interval	f(x)=4x^5-5x^4-40x^3+5 , [-3,4]	$f (x) = 4 x^{5} - 5 x^{4} - 40 x^{3} + 5$ , $[- 3, 4]$
50519	Find the Absolute Max and Min over the Interval	f(x)=5+5x-5x^2 ; [0,4]	$f (x) = 5 + 5 x - 5 x^{2}$ ; $[0, 4]$
50520	Find the Absolute Max and Min over the Interval	f(x)=5+x-x^2 ; [0,3]	$f (x) = 5 + x - x^{2}$ ; $[0, 3]$
50521	Find the Absolute Max and Min over the Interval	f(x)=6+x-x^2 ; [0,3]	$f (x) = 6 + x - x^{2}$ ; $[0, 3]$
50522	Find the Absolute Max and Min over the Interval	f(x)=6+5x-5x^2 ; [0,2]	$f (x) = 6 + 5 x - 5 x^{2}$ ; $[0, 2]$
50523	Find the Absolute Max and Min over the Interval	f(x)=6+5x-5x^2 ; [0,3]	$f (x) = 6 + 5 x - 5 x^{2}$ ; $[0, 3]$
50524	Find the Absolute Max and Min over the Interval	f(x)=6sin(x) , [0,2pi]	$f (x) = 6 \sin (x)$ , $[0, 2 π]$
50525	Find the Absolute Max and Min over the Interval	f(x)=7+5x-5x^2 ; [0,2]	$f (x) = 7 + 5 x - 5 x^{2}$ ; $[0, 2]$
50526	Find the Trig Value	sin(1/2)	$\sin (\frac{1}{2})$
50527	Find the Trig Value	sin(52 degrees )cos(13 degrees )-cos(52 degrees )sin(13 degrees )	$\sin (52 °) \cos (13 °) - \cos (52 °) \sin (13 °)$
50528	Find the Trig Value	tan(theta)=(2 square root of 3)/3sin(theta)	$\tan (θ) = \frac{2 \sqrt{3}}{3} \sin (θ)$
50529	Evaluate the Function	f(x)=2(-2)^3-24*-2	$f (x) = 2 {(- 2)}^{3} - 24 \cdot - 2$
50530	Evaluate the Function	f(x)=-5^3-12*-5	$f (x) = - 5^{3} - 12 \cdot - 5$
50531	Evaluate the Function	f(x)=x+2 , f(3)	$f (x) = x + 2$ , $f (3)$
50532	Evaluate the Function	y=f(g(x)) = cube root of 6-x^2	$y = f (g (x)) = \sqrt[3]{6 - x^{2}}$
50533	Evaluate the Function	f(x)=7x-2 , x=6	$f (x) = 7 x - 2$ , $x = 6$
50534	Find the Domain and Range	x^2+8x+7	$x^{2} + 8 x + 7$
50535	Find the Concavity	y=4x^3+21x^2+36x-20	$y = 4 x^{3} + 21 x^{2} + 36 x - 20$
50536	Find the Concavity	f'(x)=25x^2-16	$f' (x) = 25 x^{2} - 16$
50537	Find the Concavity	f'(x)=25x^2-1	$f' (x) = 25 x^{2} - 1$
50538	Find the Derivative Using Product Rule - d/d@VAR	f(x)=x^5h(x)	$f (x) = x^{5} h (x)$
50539	Find the Derivative Using Product Rule - d/d@VAR	f(x)=x^3cos(x)	$f (x) = x^{3} \cos (x)$
50540	Find the Derivative Using Product Rule - d/d@VAR	f(x)=(x-4)(4x+5)	$f (x) = (x - 4) (4 x + 5)$
50541	Find the Derivative Using Product Rule - d/d@VAR	p(y)=(y^-1+y^-2)(4y^-3-9y^-4)	$p (y) = (y^{- 1} + y^{- 2}) (4 y^{- 3} - 9 y^{- 4})$
50542	Find the Derivative Using Product Rule - d/d@VAR	p(y)=(y^-1+y^-2)(3y^-3-8y^-4)	$p (y) = (y^{- 1} + y^{- 2}) (3 y^{- 3} - 8 y^{- 4})$
50543	Find the Derivative Using Product Rule - d/d@VAR	h(z)=(3-z^2)(z^3-3z+2)	$h (z) = (3 - z^{2}) (z^{3} - 3 z + 2)$
50544	Find the Trig Value	tan(pi/4)	$\tan (\frac{π}{4})$
50545	Find the Trig Value	sin(theta)=3/5	$\sin (θ) = \frac{3}{5}$
50546	Find the Trig Value	tan(theta)=3/5	$\tan (θ) = \frac{3}{5}$
50547	Find the Trig Value	cos(theta)=-4/7	$\cos (θ) = - \frac{4}{7}$
50548	Find the Domain and Range	-2x^3+3x^2+12x-3	$- 2 x^{3} + 3 x^{2} + 12 x - 3$
50549	Find the Domain and Range	square root of 1-5^x	$\sqrt{1 - 5^{x}}$
50550	Find the Domain and Range	1/10x-1/6	$\frac{1}{10} x - \frac{1}{6}$
50551	Find the Domain and Range	log base 4 of x+1	$\log_{4} (x + 1)$
50552	Find the Domain and Range	2x^2-3x+3	$2 x^{2} - 3 x + 3$
50553	Find the Domain and Range	5t-9t^2	$5 t - 9 t^{2}$
50554	Find the Domain and Range	e^(x-3)+4	$e^{x - 3} + 4$
50555	Find the Domain and Range	x/(1- natural log of x-5)	$\frac{x}{1 - \ln (x - 5)}$
50556	Find the Domain and Range	-1/6x^2+200x	$- \frac{1}{6} x^{2} + 200 x$
50557	Find the Domain and Range	-1/7x^2+100x	$- \frac{1}{7} x^{2} + 100 x$
50558	Evaluate the Function	f(9)=x/(x^2+81)	$f (9) = \frac{x}{x^{2} + 81}$
50559	Evaluate the Function	f(3)=x^2-11	$f (3) = x^{2} - 11$
50560	Evaluate the Function	f(0.5)=9.34-21.97x+16.3x^2-3.704x^3	$f (0.5) = 9.34 - 21.97 x + 16.3 x^{2} - 3.704 x^{3}$
50561	Evaluate the Function	f(x)=(6)^3-6(6)^2-36*6	$f (x) = {(6)}^{3} - 6 {(6)}^{2} - 36 \cdot 6$
50562	Evaluate the Function	f(1/5)=15x^4-4x^3	$f (\frac{1}{5}) = 15 x^{4} - 4 x^{3}$
50563	Evaluate the Function	f(x)=3/( square root of x) , a=1/16	$f (x) = \frac{3}{\sqrt{x}}$ , $a = \frac{1}{16}$
50564	Evaluate the Function	f(5/x)=25/(x^2)	$f (\frac{5}{x}) = \frac{25}{x^{2}}$
50565	Evaluate the Function	f(0)=25/((x^2+25)^(3/2))	$f (0) = \frac{25}{{(x^{2} + 25)}^{\frac{3}{2}}}$
50566	Evaluate the Function	f(-5)=(x-3)/(x^2-9)	$f (- 5) = \frac{x - 3}{x^{2} - 9}$
50567	Evaluate the Function	f(2)=e^x	$f (2) = e^{x}$
50568	Evaluate the Function	f(4)=x+16/x	$f (4) = x + \frac{16}{x}$
50569	Evaluate the Function	f(8)=4 cube root of x	$f (8) = 4 \sqrt[3]{x}$
50570	Evaluate the Function	f(-2)=3x^2+5x-2	$f (- 2) = 3 x^{2} + 5 x - 2$
50571	Evaluate the Function	f(x)=4x^2+12+5 , a=-2	$f (x) = 4 x^{2} + 12 + 5$ , $a = - 2$
50572	Evaluate the Function	f(3)=-2x^2-4	$f (3) = - 2 x^{2} - 4$
50573	Evaluate the Function	f(6)=5x^4+5x^3-7x^2+4x-4	$f (6) = 5 x^{4} + 5 x^{3} - 7 x^{2} + 4 x - 4$
50574	Evaluate the Function	f(0)=64/((x^2+64)^(3/2))	$f (0) = \frac{64}{{(x^{2} + 64)}^{\frac{3}{2}}}$
50575	Evaluate the Function	f(-2)=2x-4	$f (- 2) = 2 x - 4$
50576	Evaluate the Function	k(-5)=6x+100	$k (- 5) = 6 x + 100$
50577	Evaluate the Function	f(1.05)=9.34-21.97x+16.3x^2-3.704x^3	$f (1.05) = 9.34 - 21.97 x + 16.3 x^{2} - 3.704 x^{3}$
50578	Evaluate the Function	f(pi/6)=sin(3x)	$f (\frac{π}{6}) = \sin (3 x)$
50579	Evaluate the Function	f(4)=4x^(5/4)+4x^(3/2)+2x	$f (4) = 4 x^{\frac{5}{4}} + 4 x^{\frac{3}{2}} + 2 x$
50580	Evaluate the Function	f(1) = cube root of -80x^3+144	$f (1) = \sqrt[3]{- 80 x^{3} + 144}$
50581	Evaluate the Function	f(x)=3x^2-4x+1 m=5	$f (x) = 3 x^{2} - 4 x + 1$ $m = 5$
50582	Evaluate the Function	f(9)=x^3-9x^2-81x	$f (9) = x^{3} - 9 x^{2} - 81 x$
50583	Evaluate the Function	f(15)=3e^x	$f (15) = 3 e^{x}$
50584	Evaluate the Function	f(- square root of 6)=(12x^2)/(x^4+36)	$f (- \sqrt{6}) = \frac{12 x^{2}}{x^{4} + 36}$
50585	Evaluate the Function	f(1)=-x^2+5x-9	$f (1) = - x^{2} + 5 x - 9$
50586	Evaluate the Function	f(3)=3x^4-20x^3+42x^2-36x	$f (3) = 3 x^{4} - 20 x^{3} + 42 x^{2} - 36 x$
50587	Evaluate the Function	f(2)=-2x+9	$f (2) = - 2 x + 9$
50588	Evaluate the Function	f(4)=(x^2)/(2+x)	$f (4) = \frac{x^{2}}{(2 + x)}$
50589	Evaluate the Function	f(0)=5/2x^2	$f (0) = \frac{5}{2} x^{2}$
50590	Evaluate the Function	f(21)=x^2+10x+500	$f (21) = x^{2} + 10 x + 500$
50591	Evaluate the Function	f(5)=-24+80x-90x^2+42x^3-8.7x^4+0.66x^5	$f (5) = - 24 + 80 x - 90 x^{2} + 42 x^{3} - 8.7 x^{4} + 0.66 x^{5}$
50592	Evaluate the Function	f(x+h)=-4h^2-5hx+1h^2x-8h^2-6h^3	$f (x + h) = - 4 h^{2} - 5 h x + 1 h^{2} x - 8 h^{2} - 6 h^{3}$
50593	Evaluate the Function	f(pi/3)=sec(x)	$f (\frac{π}{3}) = \sec (x)$
50594	Evaluate the Function	f(0)=162/((x+9)^3)	$f (0) = \frac{162}{{(x + 9)}^{3}}$
50595	Evaluate the Function	f(x)=4/( square root of x) , a=1/4	$f (x) = \frac{4}{\sqrt{x}}$ , $a = \frac{1}{4}$
50596	Evaluate the Function	f(-2)=15x^4-4x^3	$f (- 2) = 15 x^{4} - 4 x^{3}$
50597	Evaluate the Function	f(4)=4x^(5/4)+2x^(3/2)+7x	$f (4) = 4 x^{\frac{5}{4}} + 2 x^{\frac{3}{2}} + 7 x$
50598	Evaluate the Function	f( square root of 2)=x square root of 4-x^2	$f (\sqrt{2}) = x \sqrt{4 - x^{2}}$
50599	Evaluate the Function	f(-5)=1+x^2	$f (- 5) = 1 + x^{2}$
50600	Find the Derivative Using Product Rule - d/dy	(y^-1+y^-2)(6y^-3-7y^-4)	$(y^{- 1} + y^{- 2}) (6 y^{- 3} - 7 y^{- 4})$