Question

If f(x) = a |sin x| + b e^|x| + c|x³| and if f(x) is differentiable at x = 0, then

A. a = b = c = 0

B. a = 0, b = 0, c ∈ R

C. b = c = 0, a ∈ R

D. c = 0, a = 0, b ∈ R

Answer 1

Correct answer is B.

Given that f(x) = a |sinx| + b e^|x| + c|x³| and f(x) is differentiable at x = 0.

⇒ LHD = RHD at x = 0.

By L’Hospital Rule,

⇒ -(a + b) = a + b

⇒ -2(a + b) = 0

⇒ a + b = 0

This is the value for all c € R.