The graph of f ′ (x), the derivative of f of x, is continuous for all x and consists of five line segments as shown below. Given f (0) = 7, find the absolute maximum value of f (x) over the interval [0, 4].

Question

trisarahtops · Answer

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freckles · Answer

$$f(t)-f(a)=\int\limits_a^t f'(x) dx \ \implies f(t)=\int\limits_a^t f'(x) dx+f(a)$$

freckles · Answer

use your given information for (a,f(a))

freckles · Answer

like use (0,7) for (a,f(a))

trisarahtops · Answer

I plug in (0,7) for (a,f(a))?

freckles · Answer

we are given the graph of f'(x)
we can determine from f' the critical numbers of f

freckles · Answer

do you see where f' is 0?
these will be the critical numbers...

trisarahtops · Answer

Yes, I think

freckles · Answer

plug your critical numbers into the above mentioned function