007A Sample Final 3, Problem 6

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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 $f.$

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