Find the point of local maxima or local minima and the corresponding

1.	Find the point of local maxima or local minima and the corresponding local maximum and minimum value of the function: f(x) = x2
Answer» It is given that f(x) = x² By differentiating w.r.t. x f’(x) = 2x and f”(x) = 2 We know that f’(x) = 0 By substituting the values 2x = 0 where x = 0 f”(0) = 2 > 0 Hence, x = 0 is point of local minimum and f (0) = 0 is the local minimum value.

Find the point of local maxima or local minima and the corresponding local maximum and minimum value of the function: f(x) = x2

Answer»

It is given that

f(x) = x²

By differentiating w.r.t. x

f’(x) = 2x and f”(x) = 2

We know that

f’(x) = 0

By substituting the values

2x = 0 where x = 0

f”(0) = 2 > 0

Hence, x = 0 is point of local minimum and f (0) = 0 is the local minimum value.