2. Sketch the graph of the function that is continuous and has the following properties: • $f'(-2) = 0$, $f'(3) = 0$, and $f(0) = 0$. • $f'(x) > 0$ if $-2 < x < 3$ • $f'(x) < 0$ if $x < -2$ or $x > 3$ • $f''(x) > 0$ if $x < 1/2$ • $f''(x) < 0$ if $x > 1/2$
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We know that f'(2) = 0 and f'(3) = 0. This means that the function has horizontal tangents at x = 2 and x = 3. Show more…
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