Let f(x) be continuous and differentiable function for all reals.… - Vidyadip

MCQ

Let $f(x)$ be continuous and differentiable function for all reals.$f\left( {x + y} \right) = f\left( x \right) - 3xy + f\left( y \right)$. If $\mathop {\lim }\limits_{h \to 0} \frac{{f\left( h \right)}}{h} = 7$ then the value of $f'\left( x \right)$ is

A
$-3x$
B
$7$
✓
$-3x+7$
D
$2f\left( x \right) + 7$

✓

Answer

Correct option: C.

$-3x+7$

c
$f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=\lim _{h \rightarrow 0} \frac{f(x)+f(h)-3 h x-f(x)}{h}=\lim _{h \rightarrow 0} \frac{f(h)}{h}-3 x=-3 x+7$

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