Gujarat BoardEnglish MediumSTD 12 ScienceMathsDifferentiability3 Marks
Question
If $f(x)$ is defined by $f(x) x^2$. find $f(2)$.
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Answer
Given: $f(x) = x^2$.
We know a polynomial function is everywhere differentiable. Therefore f(x) is differentiable at x = 2.
$\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(2+\text{h})-\text{f}(2)}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(2+\text{h})2-22}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{(4+\text{h}2-4\text{h})-4}{\text{h}}$
$\Rightarrow\text{f}'(2)=\lim_\limits{\text{k}\rightarrow0}\text{f}\frac{\text{h}(\text{h}+4)}{\text{h}}$
$\Rightarrow\text{f}'(2)=4$
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