Chapter 4.1, Problem 1ES

In each part, sketch the graph of a function $f$ with the stated properties, and discus the sings of $f^{\prime }$ and $f^{″}$ .

(a) The function $f$ is concave up and increasing on the interval $\left(-\infty ,+\infty \right)$ .

(b) The function $f$ is concave down and increasing on the interval $\left(-\infty ,+\infty \right)$ .

(c) The function $f$ is concave up and decreasing on the interval $\left(-\infty ,+\infty \right)$ .

(d) The function $f$ is concave down and decreasing on the interval $\left(-\infty ,+\infty \right)$ .