[问答题]
$\text { Consider a function with domain } a\lt x \lt b \text {. The following diagram shows the graph of } f^{\prime} \text {, the derivative of } f \text {. }$
From the graph above p, 0 and s are x -intercepts of $f^{\prime}$ , and there is a local minimum at x=q and a local maximum at x=r .
1. Find all the values of x where the graph of f is increasing. Justify your answer.
2. Find the value of x where the graph of f has a local minimum. Justify your answer.
3. Find the value of x where the graph of f has a local maximum. Justify your answer.
4. Find the values of x where the graph of f has points of inflexion. Justify your answer.
The total area of the region enclosed by the graph of $f^{\prime}$ and the x -axis between x=p and x=s is 25 .
5. Given that f(p)+f(s)=13 , find the value of f(0) .
