Find the point of local maxima or local minima or local minima and the corresponding local maximum and minimum values of each of the following functions:

Question

Philoid · Accepted Answer

local max. value is 19 at x = 1 and local min. value is 15 at x = 3

F^’(x)=3x²-12x+9=0

⇒3(x-3)(x-1)=0

⇒ x=3,1

F^’’(x)=6x-12

F^’’(3)=18-12=6>0 , 3 is the of local min.

F^’’(1)<0, 1 is the point of local max.

F(3)=15

F(1)=19