Choose the correct answer. If f(x) = a |sinx| + b e |x| + c|x 3 | and if f(x) is differentiable at x = 0, then

Question

Philoid · Accepted Answer

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.

Hence, option B is correct.