Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
50401	Find the Maximum/Minimum Value	h(t)=68t-16t^2	$h (t) = 68 t - 16 t^{2}$
50402	Find the Maximum/Minimum Value	f(x)=2x^2-12x-6	$f (x) = 2 x^{2} - 12 x - 6$
50403	Find the Maximum/Minimum Value	f(x)=5x^2+8x-7	$f (x) = 5 x^{2} + 8 x - 7$
50404	Find the Maximum/Minimum Value	f(x)=x(16-x)	$f (x) = x (16 - x)$
50405	Find the Maximum/Minimum Value	h(t)=56t-16t^2	$h (t) = 56 t - 16 t^{2}$
50406	Find the Maximum/Minimum Value	f(x)=sin(x) , 0<=x<pi/2	$f (x) = \sin (x)$ , $0 \leq x < \frac{π}{2}$
50407	Find the Maximum/Minimum Value	f(x)=x^3-3x+11	$f (x) = x^{3} - 3 x + 11$
50408	Find the Maximum/Minimum Value	p(x)=68+310/x-0.02x	$p (x) = 68 + \frac{310}{x} - 0.02 x$
50409	Find the Maximum/Minimum Value	f(t)=t- cube root of t	$f (t) = t - \sqrt[3]{t}$
50410	Find the Maximum/Minimum Value	f(x)=x^2+5x-9	$f (x) = x^{2} + 5 x - 9$
50411	Find the Maximum/Minimum Value	f(x)=5+3x-x^2	$f (x) = 5 + 3 x - x^{2}$
50412	Find the Maximum/Minimum Value	t(t)=-0.3t^2+2.4t+98.3	$t (t) = - 0.3 t^{2} + 2.4 t + 98.3$
50413	Find the Maximum/Minimum Value	f(x)=-3x^2+6x-7	$f (x) = - 3 x^{2} + 6 x - 7$
50414	Find the Maximum/Minimum Value	f(x)=2cos(x)^3+3cos(x)	$f (x) = 2 \cos^{3} (x) + 3 \cos (x)$
50415	Find the Maximum/Minimum Value	f(x)=-3x^2+24x-6	$f (x) = - 3 x^{2} + 24 x - 6$
50416	Find the Maximum/Minimum Value	f(x)=-5x^2+8x-1	$f (x) = - 5 x^{2} + 8 x - 1$
50417	Find the Vertex	f(x)=x^2-18x+77	$f (x) = x^{2} - 18 x + 77$
50418	Find the Vertex	f(x)=x^2-16x+60	$f (x) = x^{2} - 16 x + 60$
50419	Find the Maximum/Minimum Value	g(x)=-x^3+4x^2+3x+1	$g (x) = - x^{3} + 4 x^{2} + 3 x + 1$
50420	Find Amplitude, Period, and Phase Shift	f(x)=9sec(5pix-1/4pi)	$f (x) = 9 \sec (5 π x - \frac{1}{4} π)$
50421	Determine the Possible Number of Real Roots	f(x)=x^3-3x^2-4x+12	$f (x) = x^{3} - 3 x^{2} - 4 x + 12$
50422	Find the Maximum/Minimum Value	y=3x^2-x^3	$y = 3 x^{2} - x^{3}$
50423	Find the Maximum/Minimum Value	y=4x^2+8x	$y = 4 x^{2} + 8 x$
50424	Find the Maximum/Minimum Value	R=99x^2-0.06x^3	$R = 99 x^{2} - 0.06 x^{3}$
50425	Find the Maximum/Minimum Value	y=3cos(x)	$y = 3 \cos (x)$
50426	Find the Maximum/Minimum Value	y=2x^5+5x^4-18	$y = 2 x^{5} + 5 x^{4} - 18$
50427	Find the Maximum/Minimum Value	y=arcsec(x)-6x	$y = arcsec (x) - 6 x$
50428	Find the Maximum/Minimum Value	y=x^2-6x+3	$y = x^{2} - 6 x + 3$
50429	Find the Local Maxima and Minima	y=x^3-3x^2+7x-10	$y = x^{3} - 3 x^{2} + 7 x - 10$
50430	Find the Local Maxima and Minima	y=x^4-8x^2+16	$y = x^{4} - 8 x^{2} + 16$
50431	Find the Local Maxima and Minima	y=f(x)	$y = f (x)$
50432	Find the Local Maxima and Minima	y=5x^2 natural log of x/2	$y = 5 x^{2} \ln (\frac{x}{2})$
50433	Find the Local Maxima and Minima	y=3x^5-20x^3	$y = 3 x^{5} - 20 x^{3}$
50434	Find the Local Maxima and Minima	y=2x natural log of x	$y = 2 x \ln (x)$
50435	Find the Local Maxima and Minima	y=3x square root of 16-x^2	$y = 3 x \sqrt{16 - x^{2}}$
50436	Find the Local Maxima and Minima	y=2x^4-4x^2+1	$y = 2 x^{4} - 4 x^{2} + 1$
50437	Find the Local Maxima and Minima	f(x,y)=2x^2+3xy+4y^2-6x+7y	$f (x, y) = 2 x^{2} + 3 x y + 4 y^{2} - 6 x + 7 y$
50438	Find the Local Maxima and Minima	f(x,y)=e^(xy+y-2x)	$f (x, y) = e^{x y + y - 2 x}$
50439	Find the Sum of the First 4 Terms	18 , 6 , 2	$18$ , $6$ , $2$
50440	Find the Vertices	x^2+25y^2=25	$x^{2} + 25 y^{2} = 25$
50441	Find the Vertices	36x^2+16y^2+288x-192y+576=0	$36 x^{2} + 16 y^{2} + 288 x - 192 y + 576 = 0$
50442	Find the Vertices	4x^2-16y^2=64	$4 x^{2} - 16 y^{2} = 64$
50443	Find the Vertices	4x^2-y^2-24x-6y+23=0	$4 x^{2} - y^{2} - 24 x - 6 y + 23 = 0$
50444	Find dx/dy at (0,0)	y=8xe^x , (0,0)	$y = 8 x e^{x}$ , $(0, 0)$
50445	Find dx/dy at (0,p/4)	cos(2y)=x(0,pi/4)	$\cos (2 y) = x$ $(0, \frac{π}{4})$
50446	Find dx/dy at (2,-5)	y^2-2x^3=9 ; (2,-5)	$y^{2} - 2 x^{3} = 9$ ; $(2, - 5)$
50447	Find dx/dy at (4,1)	x^3+y^3=65 , (4,1)	$x^{3} + y^{3} = 65$ , $(4, 1)$
50448	Find dx/dy at (4,4)	y^3=16x ; (4,4)	$y^{3} = 16 x$ ; $(4, 4)$
50449	Find dx/dy at (5,25)	y^2=125x ; (5,25)	$y^{2} = 125 x$ ; $(5, 25)$
50450	Find dx/dy at (-7,-5)	xy=35 , (-7,-5)	$x y = 35$ , $(- 7, - 5)$
50451	Find dx/dy at (p^+2^,p)	3sin(y)+x=y^2 ; (pi^2,pi)	$3 \sin (y) + x = y^{2}$ ; $(π^{2}, π)$
50452	Find dy/dx at (0,0)	y=8xe^x , (0,0)	$y = 8 x e^{x}$ , $(0, 0)$
50453	Find dy/dx at (0,p/3)	sin(3y)=x(0,pi/3)	$\sin (3 y) = x$ $(0, \frac{π}{3})$
50454	Find dy/dx at (0,p/4)	cos(2y)=x(0,pi/4)	$\cos (2 y) = x$ $(0, \frac{π}{4})$
50455	Find dy/dx at (1,1)	3x^2+xy+3y^2=7 , (1,1)	$3 x^{2} + x y + 3 y^{2} = 7$ , $(1, 1)$
50456	Find dy/dx at (1,1)	6x^2+xy+6y^2=13 , (1,1)	$6 x^{2} + x y + 6 y^{2} = 13$ , $(1, 1)$
50457	Find dy/dx at (1,-2)	(x^2)/2+(y^2)/8=1 , (1,-2)	$\frac{x^{2}}{2} + \frac{y^{2}}{8} = 1$ , $(1, - 2)$
50458	Find dy/dx at (-1,3)	-1x^2+1xy-2y^3=-58 (-1,3)	$- 1 x^{2} + 1 x y - 2 y^{3} = - 58$ $(- 1, 3)$
50459	Find dy/dx at (-1,7)	y=4x^2-3x ; (-1,7)	$y = 4 x^{2} - 3 x$ ; $(- 1, 7)$
50460	Find dy/dx at (2,1)	4x^2-9y^3=7 ; (2,1)	$4 x^{2} - 9 y^{3} = 7$ ; $(2, 1)$
50461	Find dy/dx at (2,1)	x^2-xy-y^2=1 (2,1)	$x^{2} - x y - y^{2} = 1$ $(2, 1)$
50462	Find dy/dx at (2,10)	x^2y-4x^3-8=0 ; (2,10)	$x^{2} y - 4 x^{3} - 8 = 0$ ; $(2, 10)$
50463	Find dy/dx at (2,p/3)	xcos(y)=1 , (2,pi/3)	$x \cos (y) = 1$ , $(2, \frac{π}{3})$
50464	Find dy/dx at (21,3)	xy-6y^2=9 , (21,3)	$x y - 6 y^{2} = 9$ , $(21, 3)$
50465	Find dy/dx at (4,1)	x^3+y^3=65 , (4,1)	$x^{3} + y^{3} = 65$ , $(4, 1)$
50466	Find dy/dx at (4,4)	y^3=16x ; (4,4)	$y^{3} = 16 x$ ; $(4, 4)$
50467	Find dy/dx at (-4,-9)	xy=36 , (-4,-9)	$x y = 36$ , $(- 4, - 9)$
50468	Find dy/dx at (5,25)	y^2=125x ; (5,25)	$y^{2} = 125 x$ ; $(5, 25)$
50469	Find dy/dx at (-7,-5)	xy=35 , (-7,-5)	$x y = 35$ , $(- 7, - 5)$
50470	Find dy/dx at (9,6)	y^4=144x ; (9,6)	$y^{4} = 144 x$ ; $(9, 6)$
50471	Find dy/dx at (p^+2^/3,p)	sin(y)+3x=y^2 ; ((pi^2)/3,pi)	$\sin (y) + 3 x = y^{2}$ ; $(\frac{π^{2}}{3}, π)$
50472	Identify the Zeros and Their Multiplicities	f(x)=x^4-8x^3-30x^2+400x-875	$f (x) = x^{4} - 8 x^{3} - 30 x^{2} + 400 x - 875$
50473	Find the Critical Points	y=-0.025x^2+5x	$y = - 0.025 x^{2} + 5 x$
50474	Find the Critical Points	y=9-3x^2-x^3	$y = 9 - 3 x^{2} - x^{3}$
50475	Find the Critical Points	y=4+3x^2-x^3	$y = 4 + 3 x^{2} - x^{3}$
50476	Find the Critical Points	y=-x^3+2x^2+4x+2	$y = - x^{3} + 2 x^{2} + 4 x + 2$
50477	Find the Critical Points	y=4x square root of 64-x^2	$y = 4 x \sqrt{64 - x^{2}}$
50478	Find the Critical Points	y=4xe^(2x)	$y = 4 x e^{2 x}$
50479	Find the Critical Points	y=5x square root of 100-x^2	$y = 5 x \sqrt{100 - x^{2}}$
50480	Find the Critical Points	y=2x^5+5x^4-13	$y = 2 x^{5} + 5 x^{4} - 13$
50481	Find the Critical Points	y=2x^3-24x^2+9	$y = 2 x^{3} - 24 x^{2} + 9$
50482	Find the Critical Points	y=-0.025x^2+3x	$y = - 0.025 x^{2} + 3 x$
50483	Find the Critical Points	h(x)=sin(2) x+cos(x) 0<x<2pi	$h (x) = \sin (2)$ $x + \cos (x)$ $0 < x < 2 π$
50484	Find the Critical Points	g(theta)=12theta-3tan(theta)	$g (θ) = 12 θ - 3 \tan (θ)$
50485	Find the Critical Points	f'(x)=9x^2+9	$f' (x) = 9 x^{2} + 9$
50486	Find dx/dy at (9,7)	(y-3)^2=4(x-5) , (9,7)	${(y - 3)}^{2} = 4 (x - 5)$ , $(9, 7)$
50487	Find dx/dy at (-1,7)	y=4x^2-3x ; (-1,7)	$y = 4 x^{2} - 3 x$ ; $(- 1, 7)$
50488	Find dx/dy at (27,3)	y^4=3x ; (27,3)	$y^{4} = 3 x$ ; $(27, 3)$
50489	Identify the Zeros and Their Multiplicities	x^4-625	$x^{4} - 625$
50490	Identify the Zeros and Their Multiplicities	f(x)=x^3+6x^2-4x-24	$f (x) = x^{3} + 6 x^{2} - 4 x - 24$
50491	Evaluate Using the Squeeze Theorem	limit as x approaches negative infinity of x+ square root of x^2+4x	$lim_{x \to - \infty} x + \sqrt{x^{2} + 4 x}$
50492	Evaluate Using the Squeeze Theorem	limit as x approaches infinity of ( square root of x+x^2)/(3x-x^2)	$lim_{x \to \infty} \frac{\sqrt{x} + x^{2}}{3 x - x^{2}}$
50493	Evaluate Using the Squeeze Theorem	limit as t approaches infinity of ( square root of t+t^2)/(5t-t^2)	$lim_{t \to \infty} \frac{\sqrt{t} + t^{2}}{5 t - t^{2}}$
50494	Convert to Polar Coordinates	(2,-6)	$(2, - 6)$
50495	Find the Absolute Max and Min over the Interval	f(x)=x^4-2x^2+7 ; [-4,4]	$f (x) = x^{4} - 2 x^{2} + 7$ ; $[- 4, 4]$
50496	Find the Absolute Max and Min over the Interval	f(x)=x^4-8x^2+5 ; [-4,4]	$f (x) = x^{4} - 8 x^{2} + 5$ ; $[- 4, 4]$
50497	Find the Absolute Max and Min over the Interval	f(x)=x^3-x^2-x+2 ; [-1,0]	$f (x) = x^{3} - x^{2} - x + 2$ ; $[- 1, 0]$
50498	Find the Absolute Max and Min over the Interval	f(x)=x^3-x^2-x+9 ; [-1,2]	$f (x) = x^{3} - x^{2} - x + 9$ ; $[- 1, 2]$
50499	Find the Absolute Max and Min over the Interval	f(x)=x+2sin(x) , (0,pi)	$f (x) = x + 2 \sin (x)$ , $(0, π)$
50500	Find the Absolute Max and Min over the Interval	f(x)=x-2cos(x) , 0<x<2pi	$f (x) = x - 2 \cos (x)$ , $0 < x < 2 π$