Find the point of local maxima or local minima or local minima and the

1.	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:f(x) = x3 - 6x2+9x+15
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

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:f(x) = x3 - 6x2+9x+15

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