If f x = x + 1 x , x ≠ 0 , then local maximum and minimum values of function f are respectively….

Step-by-step solution

We have, f x = x + 1 x , x ≠ 0 On differentiating w.r.t.x, we get f ' ( x ) = 1 - 1 x 2 f " ( x ) = For maxima or minima, we put f ' x = 0 ⇒ 1 - 1 x 2 = 0 ⇒ x 2 - 1 = 0 ⇒ x = - 1 , 1 Now, since f ' x > 0 , x ∈ - 1 - h , - 1 and f ' x < 0 , x ∈ - 1 , - 1 + h ⇒ x = - 1 is point of local maxima. and local maxima value is f - 1 = - 1 + 1 - 1 = - 2 and f ' x < 0 when x ∈ 1 - h , 1 and f ” x > 0 when x ∈ 1,1 + h ⇒ x = 1 Is point of minima. and local minima value, f 1 = 1 + 1 1 = 2