Derivatives
Integrals
Area Under a Curve
Extrema
Implicit Differentiation
100
Find y' given: y = -cos(12x2)
y' = 24x sin(12x2)
100
Find: ∫ (3x2 + 6x + 16)dx
f(x) = x3 + 3x2 + 16x + C
100
Find the area under the curve given: y=3x2, y=0, and x=3
A=27
100
find the x value or the absolute minimum of f(x)=x2+1
x=0
100
Find y' given: x2-y2=25
y'= x/y
200
Find y' given: y = 1/3x5 + 15x2 - 62
y' = 5/3x4 + 30x
200
Find: ∫7sin(x)dx
f(x) = -7cos(x) + C
200
Find the area between y=x2 from [0,4]
Area=64/3
200
Is this answer correct??
YES!
200
Find y' given: 2x3+3y3=64
y'= -2x2/3y2
300
Find y' given: y = (x2 + 2x)(3x - 1)
y' = (x2 + 2x)(3) + (3x - 1)(2x+2)
= 3x2 + 6x + 6x2 + 6x - 2x - 2
= 9x2 + 10x - 2
300
Find: ∫ [(4/x) - (5/x2) + (8/x3)]dx
f(x) = 4ln(x) + (5/x) - (4/x2) + C
300
Find the area under the curve given: x=2y2 and x=4+y2
A= 32/3
300
Find the x-values for the maximum and minimum of f(x)=(x-2)2 on the interval [1,4]
maximum: x=4
minimum: x=2
300
Find y' given: x3y3 - y = x
y'= (1-3x2y3)/ (3x3y2-1)
400
Find y' given: y = 7x3 / 2x - 11x2
y' = 7x(11x - 4) / (11x - 2)2
400
Find: ∫ [x / (x2 + 1)2]dx
f(x) = [-1 / (2x2 + 2)] + C
400
Find the area under the curve given: y=ex, y=xex, and x=0
A= e-2
400
find the relative minimum and maximum of f(x) = 2x5 + 5x4 + 10 on the interval [-3, 0]
maximum: x=-2
minimum: x=DNE
400
Find y' given: sin(y)+ x2+ 4y= cos(x)
y'= (-sin(x)-2x)/ (cos(y)+4)
500
Find y' given: [ln(3x4)] [e5x]
y' = (4e5x/x) + 5e5x(ln(3x4))
500
Find: ∫ sin10(x) cos(x) dx
f(x) = 1/11 sin11(x) + C
500
Find the area under the curve given: y=cos(x), y=sin(2x), x=0 , x= π/2
A= 1/2
500
What is the critical number of the local maximum point of f(x) = sin x + cos x in the interval [0, 2π]?
x=(π/4)
500
Find y' given: x- cos(x2) + (y2/x) +3x5 =4x3
y'= (12x4 − 15x6 + y2 − 2x3sin(x2)− x2)/ 2xy