4. Suppose we have a continuous, differentiable function \(f\) with the following properties:
\(\lim_{x \to \infty} f(x) = -2\)
\(\lim_{x \to -\infty} f(x) = -2\)
\(f'(3) = 0\)
\(f''(x) < 0\) on the interval \((1, 5)\).
\(f''(x) > 0\) on the intervals \((-\infty, 1)\) and \((5, \infty)\).
(a) (4 points) Sketch a possible graph of \(f\).
(b) (2 points) From our given information, does \(f\) definitely have an absolute maximum? If so, where
does it occur?