SOLVED:The three cases in the First Derivative Test cover the situations one commonly encounters but do not exhaust all possibilities. Consider the functions f, g , and h whose values at 0 are all 0 and, for x ≠0 , f(x)=x^4 sin(1)/(x) g(x)=x^4(2+sin(1)/(x)) h(x)=x^4(-2+sin(1)/(x)) (a) Show that 0 is a critical number of all three functions but their derivatives change sign infinitely often on both sides of 0 . (b) Show that f hat f has neither a local maximum nor a local minimum at 0, g has a local minimum, and h has a local maximum.

Oregon State University

Baylor University

Idaho State University

This textbook answer is only visible when subscribed! Please subscribe to view the answer