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Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSDerivatives2 Marks
Question
Find the derivative of f(x) = x2 − 2 at x = 10
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Answer

We have,
$\text{f(x)}=\text{x}^{2}-2$
$\because\text{f}\text{(a)}=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f}\text{(a+h)}-\text{f(a)}}{\text{h}}$
$\text{f}'(10)=\lim\limits_{\text{h}\rightarrow0}\frac{\text{f(10+h)}-\text{f(10)}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\text{(10+h)}^{2}-2-98}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{100+20\text{h}+\text{h}^{2}-100}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\text{h(20+h)}}{\text{h}}$
$=\lim\limits_{\text{h}\rightarrow0}(20+\text{h})$
$\therefore\text{f}'(10)=20$

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