Suppose f(x) is differentiable at x = 1 and `lim_(hto0) 1/hf(1+h)=5` , then f'(1) equal to

Options

A. 6
B. 5
C. 4
D. 3

Answer

B

Explanation

`f'(1) = underset(h to 0)lim ((f(1 + h) -f(1))/(h)) = underset(h to 0)lim (f(1 + h))/(h to 0) - underset(h to 0)lim(f(1))/(h)`
Given ,` underset(h to 0) lim(f( 1 + h))/(h) = 5 `
So, ` underset( h to 0) lim (f(1))/(h)` must be finite as f'(1) exist . But ` underset(hto0) lim (f(1))/(h)`
can be finite only if f (1) = 0
So, `f'(1) = underset(hto0) lim (f(1 + h))/(h) = 5` .