5. If g is differentiable at x = c, which of the following must be true? I. g is continuous at x = c. II. $lim_{x o c} g(x)$ exists. III. $lim_{x o c} frac{g(x) - g(c)}{x - c}$ exists. (A) I only (D) I and II only (B) II only (C) III only (E) I, II, and III
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Step 1: Given that the function g is differentiable at x, we know that a differentiable function must also be continuous at the point where it is differentiable. Show more…
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