Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
61601	Find the Local Maxima and Minima	f(x,y)=6-x^2-4x-y^2	$f (x, y) = 6 - x^{2} - 4 x - y^{2}$
61602	Find the Maximum/Minimum Value	r=3+3cos(theta)	$r = 3 + 3 \cos (θ)$
61603	Find the Maximum/Minimum Value	f(x,y)=x^3+y^3-3xy	$f (x, y) = x^{3} + y^{3} - 3 x y$
61604	Find the Maximum/Minimum Value	S=450A-0.05A^3	$S = 450 A - 0.05 A^{3}$
61605	Find the Maximum/Minimum Value	f(x,y)=12xy-x^3-6y^2	$f (x, y) = 12 x y - x^{3} - 6 y^{2}$
61606	Find the Maximum/Minimum Value	f(x,y)=x^2+xy+y^2-28y+261	$f (x, y) = x^{2} + x y + y^{2} - 28 y + 261$
61607	Find the Maximum/Minimum Value	f(x,y)=6xy-x^3-3y^2	$f (x, y) = 6 x y - x^{3} - 3 y^{2}$
61608	Solve Using the Quadratic Formula	12x^2-132x+252=0	$12 x^{2} - 132 x + 252 = 0$
61609	Solve Using the Quadratic Formula	12x^2-136x+289=0	$12 x^{2} - 136 x + 289 = 0$
61610	Solve Using the Quadratic Formula	12x^2-176x+484=0	$12 x^{2} - 176 x + 484 = 0$
61611	Solve Using the Quadratic Formula	2x^2+18/7x-428=0	$2 x^{2} + \frac{18}{7} x - 428 = 0$
61612	Solve Using the Quadratic Formula	-3x^2-4x+7=0	$- 3 x^{2} - 4 x + 7 = 0$
61613	Find the Eccentricity	(x^2)/25+((y-7)^2)/5=1	$\frac{x^{2}}{25} + \frac{{(y - 7)}^{2}}{5} = 1$
61614	Find the Tangent Line at (0,2)	xe^y+ye^x=2 , (0,2)	$x e^{y} + y e^{x} = 2$ , $(0, 2)$
61615	Find the Tangent Line at (3,4)	x^2+2xy-y^2+x=20 , (3,4)	$x^{2} + 2 x y - y^{2} + x = 20$ , $(3, 4)$
61616	Find the Maximum/Minimum Value	f(x)=x^2+4x+8	$f (x) = x^{2} + 4 x + 8$
61617	Find the Maximum/Minimum Value	f(x)=x^2+4x+12	$f (x) = x^{2} + 4 x + 12$
61618	Find the Maximum/Minimum Value	f(x)=2x^3+3x^2-120x	$f (x) = 2 x^{3} + 3 x^{2} - 120 x$
61619	Find the Maximum/Minimum Value	f(x)=x^2-2x-5	$f (x) = x^{2} - 2 x - 5$
61620	Find the Maximum/Minimum Value	f(x)=x^2-2x-8	$f (x) = x^{2} - 2 x - 8$
61621	Find the Maximum/Minimum Value	f(x)=x^2-14x+1	$f (x) = x^{2} - 14 x + 1$
61622	Find the Maximum/Minimum Value	f(x)=x^2-5x-1	$f (x) = x^{2} - 5 x - 1$
61623	Find the Maximum/Minimum Value	f(x)=x^2-4x+4	$f (x) = x^{2} - 4 x + 4$
61624	Find the Maximum/Minimum Value	f(x)=x^2-6x+5	$f (x) = x^{2} - 6 x + 5$
61625	Find the Maximum/Minimum Value	f(x)=x^2-8x+12	$f (x) = x^{2} - 8 x + 12$
61626	Find the Maximum/Minimum Value	f(x)=x^3-3/2x^2	$f (x) = x^{3} - \frac{3}{2} x^{2}$
61627	Find the Maximum/Minimum Value	f(x)=x^3-3x^2-9x+1	$f (x) = x^{3} - 3 x^{2} - 9 x + 1$
61628	Find the Maximum/Minimum Value	f(x)=x^4-32x^2+256	$f (x) = x^{4} - 32 x^{2} + 256$
61629	Find the Maximum/Minimum Value	g(x)=75x-x^3	$g (x) = 75 x - x^{3}$
61630	Find the Maximum/Minimum Value	p(c)=-15c(c-8)	$p (c) = - 15 c (c - 8)$
61631	Find the Maximum/Minimum Value	f(x)=2x^3+5x	$f (x) = 2 x^{3} + 5 x$
61632	Find the Maximum/Minimum Value	f(x)=3(x-e^x)	$f (x) = 3 (x - e^{x})$
61633	Find the Maximum/Minimum Value	f(x) = square root of 4-x^2	$f (x) = \sqrt{4 - x^{2}}$
61634	Find the Maximum/Minimum Value	f(x)=(5e^x+5e^(-x))/2	$f (x) = \frac{5 e^{x} + 5 e^{- x}}{2}$
61635	Find the Vertex	h(x)=-(x+11)^2+1	$h (x) = - {(x + 11)}^{2} + 1$
61636	Convert to a Mixed Number	3.8	$3.8$
61637	Find the Center and Radius	x^2-8x+y^2+12y-48=0	$x^{2} - 8 x + y^{2} + 12 y - 48 = 0$
61638	Find the Center and Radius	x^2+y^2+8x-16y+31=0	$x^{2} + y^{2} + 8 x - 16 y + 31 = 0$
61639	Find the Center and Radius	x^2+y^2+6x-10y=0	$x^{2} + y^{2} + 6 x - 10 y = 0$
61640	Find the Local Maxima and Minima	x^6+4x^5+10	$x^{6} + 4 x^{5} + 10$
61641	Find the Local Maxima and Minima	x^7-4x^5+10	$x^{7} - 4 x^{5} + 10$
61642	Find the Local Maxima and Minima	x^3-12x^2-27x+5	$x^{3} - 12 x^{2} - 27 x + 5$
61643	Find the Local Maxima and Minima	-x^3+27x-54	$- x^{3} + 27 x - 54$
61644	Find the Local Maxima and Minima	x^3-18xy+y^3	$x^{3} - 18 x y + y^{3}$
61645	Find the Local Maxima and Minima	x^5(1-x)^6	$x^{5} {(1 - x)}^{6}$
61646	Find the Local Maxima and Minima	x^3-6x^2+9x-8	$x^{3} - 6 x^{2} + 9 x - 8$
61647	Find the Local Maxima and Minima	x(x-4)^3	$x {(x - 4)}^{3}$
61648	Find the Local Maxima and Minima	x^2-2xy+4y^2-6x-6y+8	$x^{2} - 2 x y + 4 y^{2} - 6 x - 6 y + 8$
61649	Find the Local Maxima and Minima	3x^3+18x^2-405x+2	$3 x^{3} + 18 x^{2} - 405 x + 2$
61650	Find the Local Maxima and Minima	4x^3-18x^2+24x	$4 x^{3} - 18 x^{2} + 24 x$
61651	Find the Local Maxima and Minima	8x^3-6x^4	$8 x^{3} - 6 x^{4}$
61652	Find the Local Maxima and Minima	2x+4cos(x)	$2 x + 4 \cos (x)$
61653	Find the Local Maxima and Minima	2x^3-9x^2+12x-1	$2 x^{3} - 9 x^{2} + 12 x - 1$
61654	Find the Local Maxima and Minima	2x^3-3x^2-336x	$2 x^{3} - 3 x^{2} - 336 x$
61655	Find the Local Maxima and Minima	12x-6	$12 x - 6$
61656	Find the Local Maxima and Minima	square root of xe^(-x)	$\sqrt{x} e^{- x}$
61657	Find the Local Maxima and Minima	2x^3-150x^2+50000	$2 x^{3} - 150 x^{2} + 50000$
61658	Find the Inverse	y=x^3+5x-1	$y = x^{3} + 5 x - 1$
61659	Find the Inverse	y=2/3x-6	$y = \frac{2}{3} x - 6$
61660	Find the Directrix	y^2=-10x	$y^{2} = - 10 x$
61661	Find the Directrix	x^2=9y	$x^{2} = 9 y$
61662	Find the Directrix	x^2+2x+8y=15	$x^{2} + 2 x + 8 y = 15$
61663	Find the Inflection Points	f(x)=(e^x)/(7+e^x)	$f (x) = \frac{e^{x}}{7 + e^{x}}$
61664	Find the Inflection Points	f(x)=7x^6-13x^5	$f (x) = 7 x^{6} - 13 x^{5}$
61665	Find the Inflection Points	f(x)=4x^4-8x^2+12	$f (x) = 4 x^{4} - 8 x^{2} + 12$
61666	Find the Inflection Points	f(x)=3x^5-5x^4	$f (x) = 3 x^{5} - 5 x^{4}$
61667	Find the Inflection Points	f(x)=36x+3x^2-2x^3	$f (x) = 36 x + 3 x^{2} - 2 x^{3}$
61668	Find the Inflection Points	f(x)=3(x-4)^(5/3)	$f (x) = 3 {(x - 4)}^{\frac{5}{3}}$
61669	Find the Inflection Points	f(x)=3 square root of xe^(-x)	$f (x) = 3 \sqrt{x} e^{- x}$
61670	Find the Inflection Points	f(x)=10x^4-60x^2	$f (x) = 10 x^{4} - 60 x^{2}$
61671	Find the Inflection Points	f(x)=28e^x-e^(2x)	$f (x) = 28 e^{x} - e^{2 x}$
61672	Find the Inflection Points	f(x)=190+8x^3+x^4	$f (x) = 190 + 8 x^{3} + x^{4}$
61673	Find the Inflection Points	f(x)=x^4-54x^2	$f (x) = x^{4} - 54 x^{2}$
61674	Find the Inflection Points	f(x)=x^4-8x^3	$f (x) = x^{4} - 8 x^{3}$
61675	Find the Inflection Points	f(x)=x^3-2x^2	$f (x) = x^{3} - 2 x^{2}$
61676	Find the Inflection Points	f(x)=x^3-4x	$f (x) = x^{3} - 4 x$
61677	Find the Inflection Points	f(x)=x^3-6x^2+12x	$f (x) = x^{3} - 6 x^{2} + 12 x$
61678	Find the Inflection Points	f(x) = natural log of x^2+36	$f (x) = \ln (x^{2} + 36)$
61679	Find the Third Derivative	3x^5-4x^4+5x	$3 x^{5} - 4 x^{4} + 5 x$
61680	Find the Fourth Derivative	2^x	$2^{x}$
61681	Convert to Interval Notation	2x^2>7x+4	$2 x^{2} > 7 x + 4$
61682	Solve the System of @WORD	x^3<36x	$x^{3} < 36 x$
61683	Solve the System of @WORD	x^2-x-42<=0	$x^{2} - x - 42 \leq 0$
61684	Solve the System of @WORD	x^2-3x-18<0	$x^{2} - 3 x - 18 < 0$
61685	Solve the System of @WORD	x^2-3x-28<0	$x^{2} - 3 x - 28 < 0$
61686	Verify the Identity	(sin(a-b))/(cos(a)cos(b))=tan(a)-tan(b)	$\frac{\sin (a - b)}{\cos (a) \cos (b)} = \tan (a) - \tan (b)$
61687	Find the Mean	37 , 36 , 32 , 41 , 42 , 36 , 44 , 45	$37$ , $36$ , $32$ , $41$ , $42$ , $36$ , $44$ , $45$
61688	Find the Mean	26 , 40 , 38 , 36 , 42 , 40 , 40 , 36	$26$ , $40$ , $38$ , $36$ , $42$ , $40$ , $40$ , $36$
61689	Find the Mean	100 , 100 , 98 , 95 , 95 , 96 , 95 , 92 , 81 , 88	$100$ , $100$ , $98$ , $95$ , $95$ , $96$ , $95$ , $92$ , $81$ , $88$
61690	Convert to Interval Notation	x^4-37x^2+36>=0	$x^{4} - 37 x^{2} + 36 \geq 0$
61691	Convert to Interval Notation	x^2-4x-12<=0	$x^{2} - 4 x - 12 \leq 0$
61692	Solve the System of @WORD	x/3+1/6<=2x+3/2	$\frac{x}{3} + \frac{1}{6} \leq 2 x + \frac{3}{2}$
61693	Convert to Trigonometric Form	(cos((4pi)/7)+isin((4pi)/7))^5	${(\cos (\frac{4 π}{7}) + i \sin (\frac{4 π}{7}))}^{5}$
61694	Solve over the Interval	2sin(x)^2=-7sin(x)+9 , [0,2pi)	$2 \sin^{2} (x) = - 7 \sin (x) + 9$ , $[0, 2 π)$
61695	Solve over the Interval	y=e^(-x) ; [0,5]	$y = e^{- x}$ ; $[0, 5]$
61696	Find the Inflection Points	y=-x^6+6x^5-6x+17	$y = - x^{6} + 6 x^{5} - 6 x + 17$
61697	Find the Inflection Points	y=x+ log base 3 of x^2+5	$y = x + \log_{3} (x^{2} + 5)$
61698	Find the Inflection Points	y=(x^2+1)/(x^2-25)	$y = \frac{x^{2} + 1}{x^{2} - 25}$
61699	Find the Inflection Points	y=2x^3-24x-1	$y = 2 x^{3} - 24 x - 1$
61700	Find the Inflection Points	y=(x^3)/3+(x^2)/2-2x+7	$y = \frac{x^{3}}{3} + \frac{x^{2}}{2} - 2 x + 7$