When searching for the relative (local) extrema of a function that is continuous on…
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
When searching for the relative (local) extrema of a function f that is continuous on an open interval (a,b) but may have points where f′(x) fails to exist, which of the following sets of x-values must be examined?
(a) All values where f′(x)=0 \text{ or } f''(x)=0
(b) All values where f′(x)=0 \text{ or } f'(x) \text{ is undefined while } f(x) \text{ is defined}
(c) Only the values where f′(x)=0
(d) All values where f′(x)=0 \text{ or } f'(x) \text{ is undefined, plus the endpoints } a \text{ and } b