Suppose f (x) is differentiable at x = 1 and limh → 0 (1/h) f(1+h) = 5, then f '(1) equals

Question

Suppose f (x) is differentiable at x = 1 and limh → 0 (1/h) f(1+h) = 5, then f '(1) equals (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

f' (1) = limh →0 (f(1+h) -f(1)/h); As function is differentiable so it is continuous as it is given that limh →0 (f(1+h)/h) = 5 and hence f (1) = 0 Hence f'(1) = limh →0 (f(1+h)/h) = 5

Q. Suppose $f (x)$ is differentiable at x = 1 and $lim_{h \to 0}$ $\frac{1}{h}$ f(1+h) = 5, then f '(1) equals

3

4

5

6

$f^{'} (1) = lim_{h \to 0} \frac{f ( 1 + h ) - f ( 1 )}{h};$
As function is differentiable so it is continuous as it is given that
$lim_{h \to 0} \frac{f ( 1 + h )}{h}$
= 5 and hence f (1) = 0
Hence $f^{'} (1) = lim_{h \to 0} \frac{f ( 1 + h )}{h} = 5$

Q. Suppose f(x) is differentiable at x = 1 and limh→0​ h1​f(1+h) = 5, then f '(1) equals

3

4

5

6

f′(1)=limh→0​hf(1+h)−f(1)​; As function is differentiable so it is continuous as it is given that limh→0​hf(1+h)​ = 5 and hence f (1) = 0 Hence f′(1)=limh→0​hf(1+h)​=5

Q. Suppose $f (x)$ is differentiable at x = 1 and $lim_{h \to 0}$ $\frac{1}{h}$ f(1+h) = 5, then f '(1) equals

$f^{'} (1) = lim_{h \to 0} \frac{f ( 1 + h ) - f ( 1 )}{h};$
As function is differentiable so it is continuous as it is given that
$lim_{h \to 0} \frac{f ( 1 + h )}{h}$
= 5 and hence f (1) = 0
Hence $f^{'} (1) = lim_{h \to 0} \frac{f ( 1 + h )}{h} = 5$