Question

Given that f(x) and f’(x) are differentiable at x = c. The Second derivative test will fail if f”(c) is found to be zero

• A. True
• B. False

Answer 1

The correct option is A

True

If f’(c) = 0 , now according to the second derivative test, f”(c) < 0 => x = c is a maximum. If f”(c) > 0 , x = c is a minimum. But if f”(c) is found to be zero we can’t say anything about it. Thus the test fails when f"(x) is found to be zero.