Name ____________________
Calculus Derivative Review
Find f '(x) for each function:
1
1) f (x) = 4
x
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!
!
2) f (x) =
1
1 32
x " 4x2
2
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3) f (x) = x 3 cos(x)
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!
!
4) f (x) =
x
x +1
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5) f (x) = (x 3 + 7x) 3
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6) f (x) = ln(4 x 2 )
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7) f (x) = e 5x
3
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8) Find the slope of the tangent line to the graph f(x) = sin2x when x = π
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9) Find the absolute minimum and maximum on [−1, 5] of the function f (x) = (1 " x)e x
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10) Find all points of inflection on [−π, π] of the function f (x) = x cos(x)
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Name ____________________
Calculus Integration Review
Find f '(x) for each function:
2x
1) " 2 dx
x +1
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!
2)
"x
2
sin(x 3 )dx
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!
3)
" tan(x)sec (x)dx
2
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4)
!
5)
"
ln(x 2 )
dx
x
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" x sin(x)dx
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!
1
6) #
!
7)
"
9 " x2
4
0
dx
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1
dx
x
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8) Find the area between the curves f(x) = sin2(x) and g(x) = 5cos(x) over [-1, 1]
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9) Find the area between the curves f(x) = x2 and g(x) = x3
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1 32
10) Find the solid generated by revolving the line y = (x) around the x-axis over the interval [0, 5]
2
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