Question

If f is continuous everywhere, f'(3) = 0 and f" (3) = 4, then there must be a local minimum at z = 3.​

Answer 1

True

Explanation:

f'(3) = 0 says the tangent line at x = 3 is horizontal.

f"(3) = 0 means the graph of f is concave up at x = 3.

Together, these tell you the graph has a local minimum at x = 3. The graph is U-shaped at the point where x = 3.