If given table of x and slope of each x, why would it be incorrect to say that the function is increasing?

Question

Let's say that we are given the information below

$$\begin{array}{|c|c|c|c|c|c|} \hline x & -2 & 0 & 3 & 5 & 6 \\\hline f'(x) & 3 & 1 & 4 & 7 & 5 \\\hline \end{array}$$

We can see that all of the slopes are positive. So I come to the conclusion that the function increases from $(-2,6)$. However, my textbook states that it is incorrect. Why is this?

Answer 1

Clearly, $f'(x)$ represents the slope, which can decrease at the intermediate points. It need not be monotonous, it may fluctuate.