Q. 95.0( 1 Vote )

Choose the correct answer.

If f(x) = a |sinx| + 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 ϵ R

C. b = c = 0, a ϵ R

D. c = 0, a = 0, b ϵ R

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.

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