Suppose f(x) is continuous on [4,5] and −4≤f′(x)≤5 for all x in (4,5). Use the Mean Value Theorem to estimate f(5)−f(4).

Answer 1

(f(5) - f(4) = f'(c)(5 -4 ),= f'(c) were 4 < c < 5

So, - 4 ≤ f(5) - f(4) ≤ 5