009A Sample Final 3, Problem 6

Let

$f(x)=4+8x^{3}-x^{4}$

a) Over what $x$-intervals is $f$ increasing/decreasing?

b) Find all critical points of $f$ and test each for local maximum and local minimum.

c) Over what $x$-intervals is $f$ concave up/down?

d) Sketch the shape of the graph of $f.$

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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