Question

Consider the graph of the first derivativef' (2) provided below: 3 N 0 2 3 -2 The image can be also be accessed here: Graphot CLDE Use the provided graph of the first derivative f'(x) to answer each of the following questions about the function (3) Unjustihed answers will not receive full credit. You may use represent oo as infand-o as inf" if applicable. (a) on what intervalls) of axis (2) decreasing? Explain how you know (b) At what values of a does /(x) have local minimums? Explain how you know. (cl On what intervalls) of wis / (x) concave down? Explain how you know. (d) Identify all of the x-coordinates of the inflection points of/ (). Explain how you know. HTML Editor

Answer 1

Providod. a consider the graph of the first derivative fose) f(x) is decreasing on the intervals (-1.4,0) U (0, 1.4) x-coordinates of the inflection points of the @ Explainations ": f'(x) is negative for all HE(-1.9,0) U (0, 1.4) f'(x) <0 + Xe (-)• 4,0) 0(+, -4). (6 f(x) has a local minimum at x=114 Explainations - fx) has a x=1.4, -1, f) has a local minimum at because f'(x) so for xe 1.4 and f'(x) >0 for xylot. So, my first derivative test, of has a local minimum at gea14 © flow is concave down on the intervals (-2, -1) (16,1) on (-2,-1) Explaination! f(x) is concave down on (-2,-1)0(0, 1) because graph of f'(x) decreasing V10,1). — (f'(x)) = f'pol) 50,#xel-2,-1)"(0,1) 1 d Explaination - fowl are f(x) has the inflection points at the x=-1, oil, because fix) chango It's direction (increasing / decreality) at these Rolent