Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be:

g(x) = x³ – 3x

g(x) = x³ – 3x

⇒ g’(x) = 3x² - 3

Now, g’(x) = 0

⇒ 3x² - 3 = 0

⇒ 3x² = 3

⇒ x = � 1

g’’(x) = 6x

Now, g’(1) = 6>0

and g’(-1) = -6 < 0

Then, by second derivative test,

⇒ x = 1 is point of local maxima and local minima of g at x = 1 is

g(1) = 1³ – 3 = 1-3 =-2

And,

x = -1 is point of local maxima and local maximum value of g at x = -1 is

g(-1) = (-1)³ – 3(-1) = -1+3 = 2