The graph of $f'$, the derivative of the function $f$, is shown above for $0\leq x\leq 20$. The area of the regions between the graph of $f'$ and the $x$-axis are $15$, $12$, and $4$ respectively. If $f(0)=5$, what is the maximum value of $f$ on the closed interval $0\leq x\leq 20$ ?

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The value of $f$ can be given by the following integral:

$$f(x) = f(0) + \int \limits_0^x f'(x)  dx$$

Note that for areas under the curve, the values are negative.

The maximum value will be obtained by taking only the first region under the curve:

$$\text{Max} = f(0)+15$$ $$= 5+15 =\boxed{20}$$