If f'(a)=0 and f''(a)<0, what occurs at x=a?

A. Local maximum

Step 1: Identify the second derivative test. Step 2: f'(a)=0 gives a critical point and f''(a)<0 means the curve bends downward, so it is a local maximum. Step 3: Memory tip: Negative second derivative means maximum.

Step 1: अवधारणा second derivative test है। Step 2: f'(a)=0 critical point देता है और f''(a)<0 curve को downward बनाता है, इसलिए local maximum होता है। Step 3: याद रखें: second derivative negative means maximum।