Let $f(x)$ be a differentiable function at $x = a$ with $f'(a) = 2$ and $f(a) = 4$. Then, $\mathop {\lim }\limits_{x \to a} \frac{{xf(a) - af(x)}}{{x - a}}$ equals

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

Let

f(x)

be a differentiable function at

x = a

with

f'(a) = 2

and

f(a) = 4

. Then,

\lim\limits_{x \to a} \frac{{xf(a) - af(x)}}{{x - a}}

equals

View answer and explanation

Correct option: B

4 - 2a

Option B (4 - 2a) is correct because it is the result of applying L'Hopital's rule or using the definition of the derivative to evaluate the limit.

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