Q. 95.0( 1 Vote )

# 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

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|x^{3}| 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.

Rate this question :

If then is equal to

Mathematics - ExemplarDifferentiate each of the following w.r.t. x

Mathematics - Exemplar

Differentiate each of the following w.r.t. x

Mathematics - Exemplar

Differentiate each of the following w.r.t. x

Mathematics - Exemplar

Differentiate the following functions with respect to x:

e^{tan 3x}

Differentiate each of the following w.r.t. x

Mathematics - Exemplar

Differentiate each of the following w.r.t. x

Mathematics - Exemplar

Differentiate the following functions with respect to x:

log(cosec x – cot x)

RD Sharma - Volume 1Differentiate the following functions with respect to x:

RD Sharma - Volume 1

Differentiate each of the following w.r.t. x

(x + 1)^{2} (x + 2)^{3} (x + 3)^{4}