Question

If $ f:R\to R $ be a differentiable function such that $ f(4)=6 $ and $ f'(4)=2, $ then $ \underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{x\,\,f(4)-4f(x)}{x-4} $ is equal to

• A. $ 2 $
• B. $ -2 $
• C. $ 0 $
• D. $ 1 $

Answer 1

Answer: (B)

$ \underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{x\,f(4)-4f(x)}{x-4} $
$ =\underset{x\to 4}{\mathop{\lim }}\,\,\,\frac{f(4)-4f'(x)}{1} $
$ =f(4)-4f'(4) $ $ =\frac{6-4(2)}{1}=6-8 $
$ =-2 $