Pls answer math hard

Suppose that f(0) = −3 and f '(x) ≤ 8 for all values of x. how large can f(4) possibly be? solution we are given that f is differentiable (and therefore continuous) everywhere. in particular, we can apply the mean value theorem on the interval [0, 4] . there exists a number c such that

Using the side-splitter theorem, daniel wrote a proportion for the segment formed by luke segment de. what is ec?

In triangle △abc, ∠abc=90°, bh is an altitude. find the missing lengths. ah=4 and hc=1, find bh.