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:

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