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) = x4 - 62x2+120x+9
Answer» local max. value is 68 at x = 1 and local min. values are−1647 at x = −6 and −316 at x = 5 F’(x) = 4x³- 124x+120 = 0 ⇒ 4(x³- 31x+30) = 0 For x = 1, the given eq is 0 x -1 is a factor, 4(x -1)(x+6)(x -5) = 0 ⇒ X = 1, -6,5 F’’(1))<0, 1 is the point of max. F’’(-6) and f ’’(5) 0, -6 and 5 are point of min. F(1) = 68 F(-6) = -1647 F(5) = -316

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) = x4 - 62x2+120x+9

Answer»

local max. value is 68 at x = 1 and local min. values are−1647 at x = −6 and −316 at x = 5

F’(x) = 4x³- 124x+120 = 0

⇒ 4(x³- 31x+30) = 0

For x = 1, the given eq is 0

x -1 is a factor,

4(x -1)(x+6)(x -5) = 0

⇒ X = 1, -6,5

F’’(1))<0, 1 is the point of max.

F’’(-6) and f ’’(5) 0, -6 and 5 are point of min.

F(1) = 68

F(-6) = -1647

F(5) = -316