Sol. We have,

f(x) = dt

⇒ f ′ (x) = (x 2 ) –0

⇒ f ′ (x) =

⇒ f ′ (x) =

Now, f ′ (x) = 0 ⇒ x = 0, 1, –1, 2, –2 The changes in signs of f ′ (x) for different values of x are shown in fig. below

Clearly, f ′ (x) changes its sign from positive to negative in the neighbourhoods of the points x = –1, 1. S, x = 1 and x = –1 are points of local maxima. Also, f ′ (x) changes its sign from negative to positive in the neighbourhood of x = –2, 0 and 2. So, x = –2, 0, 2 are the points of local minimum.