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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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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