Chapter 4.2, Problem 1ES

In each part, sketch the graph of a continuous function $f$ with the stated properties.

(a) $f$ is concave up on the interval $\left(-\infty ,+\infty \right)$ and has exactly one relative extremum.

(b) $f$ is concave up on the interval $\left(-\infty ,+\infty \right)$ and has no relative extrema.

(c) The function $f$ has exactly two relative extrema on the interval $\left(-\infty ,+\infty \right),$ and $f\left(x\right)\to +\infty$ as $x\to +\infty$ .

(d) The function $f$ has exactly two relative extrema on the interval $\left(-\infty ,+\infty \right),$ and $f\left(x\right)\to -\infty$ as $x\to +\infty$ .