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  • Let f(x) be a twice-differentiable function and <img alt="\mathrm{f}^{\prime

Let f(x) be a twice-differentiable function and \mathrm{f}^{\prime \prime}(0)=2 then  \lim _{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^{2}} is 

Option: 1

6


Option: 2

3


Option: 3

12


Option: 4


none of these


Answers (1)

best_answer

\text { Limit } =\lim _{x \rightarrow 0} \frac{2 f^{\prime}(x)-6 f^{\prime}(2 x)+4 f^{\prime}(4 x)}{2 x} \\

=\lim _{x \rightarrow 0} \frac{2 f^{\prime \prime}(x)-12 f^{\prime \prime}(2 x)+16 f^{\prime \prime}(4 x)}{2}=\frac{6 f^{\prime \prime}(0)}{2}=6

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