Question 296 of 401MediumMCQ
Suppose f(x) is differentiable at x = 1 and
\[\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) = 5\], then \[f'\left( 1 \right)\] equals Solutions · 1
Official solution
\[f'\left( 1 \right) = \mathop {\lim }\limits_{h \to 0} {{f\left( {1 + h} \right) - f\left( 1 \right)} \over h};\]
As function is differentiable so it is continuous as it
is given that \[\mathop {\lim }\limits_{h \to 0} {{f\left( {1 + h} \right)} \over h} = 5\] and hence f(1)=0
Hence f′(1) \[ = \mathop {\lim }\limits_{h \to 0} {{f\left( {1 + h} \right)} \over h} = 5\] Answer the question to unlock