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  • If exists and non-zero then <img alt="\mathrm{\lim _{h \rightarrow 0} \frac{f(c+h)+f(c-h)

If f^{\prime}(c) exists and non-zero then \mathrm{\lim _{h \rightarrow 0} \frac{f(c+h)+f(c-h)-2 f(c)}{h}}  is equal to

Option: 1

f^{\prime}(c)


Option: 2

0


Option: 3

2 f^{\prime}(c)


Option: 4

none of these


Answers (1)

best_answer

\mathrm{\lim _{h \rightarrow 0} \frac{f(c+h)+f(c-h)-2 f(c)}{h}}
 

\mathrm{=\lim _{h \rightarrow 0} \frac{f(c+h)-f(c)}{h}+\frac{f(c-h)-f(c)}{h} }
\mathrm{=f^{\prime}(c)-\lim _{h \rightarrow 0} \frac{f(c-h)-f(c)}{-h} }
\mathrm{=f^{\prime}(c)-f^{\prime}(c)=0}

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Sayak

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