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how to prove a function is differentiable on an interval

There is actually a very simple way to understand this physically. exist and f' (x 0 -) = f' (x 0 +) Hence. Learn how to determine the differentiability of a function. If f is differentiable on the interval [a, b] and f^{\prime}(a)<00 {/eq} for all numbers x in I except for a single number c. Prove that f is increasing on the entire interval I. Monotonicity of a Function: prove that f^{\prime}(x) must vanish at at least n-1 points in I f(x1)

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