Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
54001	Find the Local Maxima and Minima	5x^2+4x-9	$5 x^{2} + 4 x - 9$
54002	Find the Local Maxima and Minima	5cos(x)^2-10sin(x)	$5 \cos^{2} (x) - 10 \sin (x)$
54003	Find the Local Maxima and Minima	4x^3+48x^2+180x	$4 x^{3} + 48 x^{2} + 180 x$
54004	Find the Local Maxima and Minima	-x^3-12x^2-45x+1	$- x^{3} - 12 x^{2} - 45 x + 1$
54005	Find the Local Maxima and Minima	2x^3-39x^2+216x	$2 x^{3} - 39 x^{2} + 216 x$
54006	Find the Local Maxima and Minima	-x^3+4x^2+16x-2	$- x^{3} + 4 x^{2} + 16 x - 2$
54007	Find the Local Maxima and Minima	x^3-12x+600	$x^{3} - 12 x + 600$
54008	Find the Local Maxima and Minima	-2x-1	$- 2 x - 1$
54009	Find the Local Maxima and Minima	6-(8+7x)^(2/7)	$6 - {(8 + 7 x)}^{\frac{2}{7}}$
54010	Find the Local Maxima and Minima	(x^2-9x+39)/(x-7)	$\frac{x^{2} - 9 x + 39}{x - 7}$
54011	Find the Local Maxima and Minima	4x+500000/x	$4 x + \frac{500000}{x}$
54012	Find the Local Maxima and Minima	sin(x)-cos(x)	$\sin (x) - \cos (x)$
54013	Find the Local Maxima and Minima	6x+18	$6 x + 18$
54014	Find the Local Maxima and Minima	2x^3+18x^2+30x+2	$2 x^{3} + 18 x^{2} + 30 x + 2$
54015	Find the Local Maxima and Minima	5x square root of 64-x^2	$5 x \sqrt{64 - x^{2}}$
54016	Find the Center and Radius	x^2+y^2-2x-80=0	$x^{2} + y^{2} - 2 x - 80 = 0$
54017	Find the Center and Radius	(x-8)^2+(y+6/5)^2=25/9	${(x - 8)}^{2} + {(y + \frac{6}{5})}^{2} = \frac{25}{9}$
54018	Find the Center and Radius	x^2+y^2+8x+14y=-56	$x^{2} + y^{2} + 8 x + 14 y = - 56$
54019	Find the Directrix	(x-3)^2=8(y-4)	${(x - 3)}^{2} = 8 (y - 4)$
54020	Find the Points of Intersection	y=x^3-9x , y=-(x-3)	$y = x^{3} - 9 x$ , $y = - (x - 3)$
54021	Find the Inverse	y=12+0.75x	$y = 12 + 0.75 x$
54022	Find the Inverse	y = log base 1/2 of x	$y = \log_{\frac{1}{2}} (x)$
54023	Find the Inverse	x=7y^7-3y^3+y+8	$x = 7 y^{7} - 3 y^{3} + y + 8$
54024	Find the Inverse	y=2x^2-8x	$y = 2 x^{2} - 8 x$
54025	Find the Inverse	y=9x+9	$y = 9 x + 9$
54026	Find the Center and Radius	x^2+y^2-10x+4y=-25	$x^{2} + y^{2} - 10 x + 4 y = - 25$
54027	Find the Center and Radius	x^2+y^2-12x+6y+29=0	$x^{2} + y^{2} - 12 x + 6 y + 29 = 0$
54028	Find the Center and Radius	x^2+(y-3)^2=18	$x^{2} + {(y - 3)}^{2} = 18$
54029	Find the Center and Radius	x^2+y^2+4x-6y+14=0	$x^{2} + y^{2} + 4 x - 6 y + 14 = 0$
54030	Find the Center and Radius	3(x-5)^2+3(y+9)^2=48	$3 {(x - 5)}^{2} + 3 {(y + 9)}^{2} = 48$
54031	Find the Center and Radius	x^2+y^2+2x-6y+11=0	$x^{2} + y^{2} + 2 x - 6 y + 11 = 0$
54032	Find the Center and Radius	x^2+y^2-4x+2y=0	$x^{2} + y^{2} - 4 x + 2 y = 0$
54033	Find the Center and Radius	x^2+y^2-4x-6y+13=0	$x^{2} + y^{2} - 4 x - 6 y + 13 = 0$
54034	Find the Center and Radius	x^2+y^2+2x+4y-44=0	$x^{2} + y^{2} + 2 x + 4 y - 44 = 0$
54035	Find the Inverse	y=0.3^x	$y = {0.3}^{x}$
54036	Find the Inverse	y=200(1.03)^x	$y = 200 {(1.03)}^{x}$
54037	Find the Inverse	y=1+e^x	$y = 1 + e^{x}$
54038	Find the Inverse	y = log base 6 of 4x+4	$y = \log_{6} (4 x + 4)$
54039	Find the Inverse	y = natural log of x+1	$y = \ln (x + 1)$
54040	Find the Inverse	y = square root of 1/(x-2)	$y = \sqrt{\frac{1}{x - 2}}$
54041	Find the Inverse	Y=X^3+2X-1	$Y = X^{3} + 2 X - 1$
54042	Find the Range	56 , 61 , 52 , 69 , 64 , 46 , 54	$56$ , $61$ , $52$ , $69$ , $64$ , $46$ , $54$
54043	Find the Directrix	(x+2)^2=-4(y-1)	${(x + 2)}^{2} = - 4 (y - 1)$
54044	Find the Directrix	x^2=-28y	$x^{2} = - 28 y$
54045	Find the Directrix	y^2=32x	$y^{2} = 32 x$
54046	Find the Points of Intersection	x^2-xy+y^2=10 2x^2+xy-y^2=20	$x^{2} - x y + y^{2} = 10$ $2 x^{2} + x y - y^{2} = 20$
54047	Find the Symmetry	f(x)=-2x^4-4x^3	$f (x) = - 2 x^{4} - 4 x^{3}$
54048	Simplify/Condense	1/8 natural log of x+ natural log of y	$\frac{1}{8} \ln (x) + \ln (y)$
54049	Simplify/Condense	natural log of 8- natural log of 2	$\ln (8) - \ln (2)$
54050	Simplify/Condense	1/2 natural log of 8-1/2 natural log of 2	$\frac{1}{2} \ln (8) - \frac{1}{2} \ln (2)$
54051	Simplify/Condense	1/3( natural log of x+ natural log of y)-4 natural log of z	$\frac{1}{3} (\ln (x) + \ln (y)) - 4 \ln (z)$
54052	Find the Local Maxima and Minima	9x^6-13x^5	$9 x^{6} - 13 x^{5}$
54053	Find the Local Maxima and Minima	6x+100000/x	$6 x + \frac{100000}{x}$
54054	Find the Local Maxima and Minima	x^3-18x^2+105x+10	$x^{3} - 18 x^{2} + 105 x + 10$
54055	Find the Local Maxima and Minima	-x^3+3x-1	$- x^{3} + 3 x - 1$
54056	Find the Local Maxima and Minima	2x^3-21x^2-108x	$2 x^{3} - 21 x^{2} - 108 x$
54057	Find the Local Maxima and Minima	t square root of 64-t^2	$t \sqrt{64 - t^{2}}$
54058	Find the Local Maxima and Minima	6x^2+12x-8	$6 x^{2} + 12 x - 8$
54059	Find the Local Maxima and Minima	2x^3-6x^2-90x+9	$2 x^{3} - 6 x^{2} - 90 x + 9$
54060	Find the Local Maxima and Minima	(3x)/( square root of x-4)	$\frac{3 x}{\sqrt{x - 4}}$
54061	Find the Local Maxima and Minima	(3x)/( square root of x-6)	$\frac{3 x}{\sqrt{x - 6}}$
54062	Find the Local Maxima and Minima	x^3-3x^2+3x-4	$x^{3} - 3 x^{2} + 3 x - 4$
54063	Find the Local Maxima and Minima	x^5-15x^3	$x^{5} - 15 x^{3}$
54064	Find the Local Maxima and Minima	2x^2+4000/x+10	$2 x^{2} + \frac{4000}{x} + 10$
54065	Find the Local Maxima and Minima	((x-1)^2)/(x^2+1)	$\frac{{(x - 1)}^{2}}{x^{2} + 1}$
54066	Find the Local Maxima and Minima	0.0025x+80+10000/x	$0.0025 x + 80 + \frac{10000}{x}$
54067	Find the Local Maxima and Minima	(-1/4)(x-2)^(8/3)+4(x-2)^(2/3)	$(- \frac{1}{4}) {(x - 2)}^{(\frac{8}{3})} + 4 {(x - 2)}^{(\frac{2}{3})}$
54068	Find the Local Maxima and Minima	2x^3-33x^2+168x+7	$2 x^{3} - 33 x^{2} + 168 x + 7$
54069	Find the Local Maxima and Minima	1/5x^5+7/2x^4+71/3x^3+77x^2+120x	$\frac{1}{5} x^{5} + \frac{7}{2} x^{4} + \frac{71}{3} x^{3} + 77 x^{2} + 120 x$
54070	Find the Local Maxima and Minima	x^3+3x^2-9x-7	$x^{3} + 3 x^{2} - 9 x - 7$
54071	Find the Local Maxima and Minima	x^3-9x^2-120x+6	$x^{3} - 9 x^{2} - 120 x + 6$
54072	Find the Local Maxima and Minima	2x+700000/x	$2 x + \frac{700000}{x}$
54073	Find the Local Maxima and Minima	16x+81/x	$16 x + \frac{81}{x}$
54074	Find the Local Maxima and Minima	x^4-50x^2	$x^{4} - 50 x^{2}$
54075	Find the Local Maxima and Minima	(3e^x)/(x^3)	$\frac{3 e^{x}}{x^{3}}$
54076	Find the Local Maxima and Minima	14x+17x^(14/17)	$14 x + 17 x^{\frac{14}{17}}$
54077	Find the Local Maxima and Minima	2-x^(2/3)	$2 - x^{\frac{2}{3}}$
54078	Find the Local Maxima and Minima	(24t)/(t^2+144)	$\frac{24 t}{t^{2} + 144}$
54079	Find the Local Maxima and Minima	-x^3-7x^2-16x-42	$- x^{3} - 7 x^{2} - 16 x - 42$
54080	Find the Local Maxima and Minima	(16x^2+25)/x	$\frac{16 x^{2} + 25}{x}$
54081	Find the Local Maxima and Minima	4x square root of 2-x	$4 x \sqrt{2 - x}$
54082	Find the Local Maxima and Minima	x^3-27x+45	$x^{3} - 27 x + 45$
54083	Find the Local Maxima and Minima	x square root of 18-x^2	$x \sqrt{18 - x^{2}}$
54084	Find the Local Maxima and Minima	6x square root of 16-x^2	$6 x \sqrt{16 - x^{2}}$
54085	Find the Local Maxima and Minima	2x+x^2	$2 x + x^{2}$
54086	Find the Local Maxima and Minima	2x^2+864/x+5	$2 x^{2} + \frac{864}{x} + 5$
54087	Find the Local Maxima and Minima	10cos(x)+5sin(2x)	$10 \cos (x) + 5 \sin (2 x)$
54088	Find the Local Maxima and Minima	2x^2+3xy+4y^2+7x+11y	$2 x^{2} + 3 x y + 4 y^{2} + 7 x + 11 y$
54089	Find the Local Maxima and Minima	16x+25/x	$16 x + \frac{25}{x}$
54090	Find the Local Maxima and Minima	2x^3-33x^2+108x	$2 x^{3} - 33 x^{2} + 108 x$
54091	Find the Local Maxima and Minima	1/2x^4-4x^2+7	$\frac{1}{2} x^{4} - 4 x^{2} + 7$
54092	Find the Local Maxima and Minima	x^3-6x^2+9x+9	$x^{3} - 6 x^{2} + 9 x + 9$
54093	Find the Local Maxima and Minima	4x^3-6x^2-144x+3	$4 x^{3} - 6 x^{2} - 144 x + 3$
54094	Find the Local Maxima and Minima	-1/3x^3+2x^2-3x-12	$- \frac{1}{3} x^{3} + 2 x^{2} - 3 x - 12$
54095	Find the Local Maxima and Minima	(x+4)/(x^2-3x-28)	$\frac{x + 4}{x^{2} - 3 x - 28}$
54096	Find the Local Maxima and Minima	x^4-32x^2+8	$x^{4} - 32 x^{2} + 8$
54097	Find the Local Maxima and Minima	x^3-27x+9	$x^{3} - 27 x + 9$
54098	Find the Local Maxima and Minima	2x^2+864/x+6	$2 x^{2} + \frac{864}{x} + 6$
54099	Find the Local Maxima and Minima	-x/(5x^2+1)	$- \frac{x}{5 x^{2} + 1}$
54100	Find the Local Maxima and Minima	2x^2+256/x+7	$2 x^{2} + \frac{256}{x} + 7$