Question

Find the local minima and the local maxima ( if any ) for the function g(x) = x3 – 3x.​

Answer 1

Answer:

f

′

(x)=3x

2

−3

=0

Or

x

2

−1=0

Or

x=±1 .

f

′′

(x)=6x

Hence f

′′

(−1)<0 maxima.

f

′′

(1)>0 ... minima.

Hence f(x) attains the maximum value at x=−1 and a minimum value at x=1

f(−1)=3−1=2.

The maximum value is 2