Question

Suppose a continuous function g(x) has the four properties below. Then which of the following must be true? • g(x) has exactly two critical points at x = -1 and x = 5 • g'(-2) = 5 • g'(0) = -1 • g'(6) = -5 Select one: There is a local maximum at x = -1 and a local minimum at x = 5 o o There is a local maximum at x = -1 and x = 5 is neither a local maximum nor a local minimum There is a local minimum at x = -1 and a local maximum at x = 5 There is a local minimum at x = -1 and x = 5 is neither a local maximum nor a local minimum

Answer 1

giver . glory hey exactly two critical point at n-al and a= 5 and 5 : + 1 5 C 9 161 = -5 So is mE (-00, -1) Then glem 2,0 (: g(-2) = 570) so gemp is increasing in this interal. it ne 1-1,5) Then g'om so 1: gio)=-1<0) 80 gimi ùs decreuing. it ne (5,0) Then generoso (e so 9161=-5 co so 912) is decreusing We know that any function ma'attain maxina where the suretion changes direction from increasing to decreasing and minima where fuetion changes diration from decreasing to increasing so at naut, geng changes sign from increasing to - decreasing Hence may be a maximum point forg But at n=-5 gens does not change sign so gens in neither a local minima or local maxima. Option B is true.. Nok - If you have any doubt Please comment me.