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:
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, 1is 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
1