Question

The set of all those points, where the function f(x)=x1+|x| is differentiable, is

A

(,)

B

[0, ]

C

(,0)(0,)

D

(0,)

Solution

The correct option is B (−∞,∞) Let h(x)=x,xϵ(−∞,∞);g(x)=1+|x|,xϵ(−∞,∞) Here h is differentiable in (−∞,∞) but |x| is not differentiable at x=0. Therefore g is differentiable in (−∞,0)∪(0,∞) and g(x)≠0,∀x∈(−∞,∞). ∴f(x)=h(x)g(x)=x1+|x| It is differentiable in (−∞,0)∪(0,∞) for x = 0 limh→0f(h)−f(0)h−0=limh→0h1+|h|h=limh→011+|h|=1 Therefore f is differentiable at x = 0, so f is differentiable in (−∞,∞). Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More