Chapter 10.2, Problem 27E

(a)

To determine

The region where the graph of $f\left(x\right)$ is concave up and down in the graph of the function $f\text{'}\left(x\right)=4x-x^2$ provided as follows:

(b)

To determine

To calculate: The points of inflection of $f\left(x\right)$ for the provided graph of a function $f\text{'}\left(x\right)=4x-x^2$.

(c)

To determine

To calculate: The value of the function $f^{″}\left(x\right)$ then to graph the function and then using the graph locate where the function is concave up and down and where $f\left(x\right)$ has points of inflection for the provided graph of a function $f\text{'}\left(x\right)=4x-x^2$.

(d)

To determine

To graph: The function $f\left(x\right)$ for the provided graph of a function $f^{\prime }\left(x\right)=4x-x^2$.