Given f(x) = 3x
4 − 16x
3 + 18x
2
, x ∈ [−1, 4] .
(a) (5 points) Find all of the critical points.
(b) (10 points) Determine all of the extrema and determine its type.
(c) (5 points) Determine all of the inflection points.
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- Determine the antiderivatives for each function given below. The antiderivative is the indefinite integral of f(x), Z
f(x) dx = F(x) + C
(a) (5 points) f(x) = 3x
2 + 5x + 2
(b) (5 points) f(x) = 4 cos 2x
(c) (10 points) f = −2 sin 4x.
(d) (5 points) f(x) = −6e
3x
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Figure 1: 1 - Answer the questions below given the graph of f(x) = 3x + 2, x ∈ [0, 4] .
(a) (5 points) Find the area under the curve.
(b) (5 points) Find the area under the curve by evaluating,
Z 4
0
3x + 2 dx.
(c) (5 points) Determine the value(s) of (x, y) where the tangent line is horizontal.