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) = -(x -1)3(x+1)2
Answer» local max. value is 0 at each of the points x = 1 and x = −1 and local min. value is -3456/3125 at x = -1/5 F’(x) = -(x -1)³2(x+1) - 3(x -1)²(x+1)²= 0 ⇒ x = 1, -1, -1/5 Since, f \|\| (1) and f \|\| (-1)<0, 1 and -1 are the point of local max. F \|\| (-1/5)>0, -1/5 is the point of local min. F(1) = f(-1) = 0 Also, f(-1/5) = -3456/3125

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) = -(x -1)3(x+1)2

Answer»

local max. value is 0 at each of the points x = 1 and x = −1 and local min. value is -3456/3125 at x = -1/5

F’(x) = -(x -1)³2(x+1) - 3(x -1)²(x+1)²= 0

⇒ x = 1, -1, -1/5

Since, f || (1) and f || (-1)<0, 1 and -1 are the point of local max.

F || (-1/5)>0, -1/5 is the point of local min.

F(1) = f(-1) = 0

Also, f(-1/5) = -3456/3125