Extrema can be found where the function changes from rising to falling or vice versa see monotonicity. If you are going up a hill and want to find its highest point it would be right before the hill begins to decline again. Absolute Extrema Consider the function fx x2 1 over the interval.
Second Derivative Test Let fand f exist at every point on the interval abcontaining cand fc 0.
You remember how to find local extrema maxima or minima of a single variable function f x. Then the first step is to find the critical points x a where f a 0. How can I solve this problem. If you are going up a hill and want to find its highest point it would be right before the hill begins to decline again.