For each of the following statements, determine whether it is true or false and justify your answer. a) if the differentiable function f: R -> R is strictly increasing then f'(x) > 0 for all x. b) if the differentiable function f: R -> R is monotonically increasing, then f'(x) >= 0 for all x. c) if the function f: R -> R is differentiable and f(x) <= f(0) for all x in [-1,1] then f'(0) = 0. d) if the function f: R -> R is differentiable and f(x) <= f(1) for all x in [-1,1], then f'(1) = 0.
Explanation / Answer
true c) if the function f: R -> R is differentiable and f(x)