If f x - x - then f - x - where x-0 is equal toA- 1B- -1C- 0D- -x-x

The correct option is D |x|/x∵ f(x)={ x,x≥ 0 x,x lt;0 . ∵ f'(x)={ 1,x gt;0,i.e,|x|/x,x gt;0 1,x gt;0,i.e,|x|/x,x gt;0. =|x|/x,x≠ 0 ...

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Standard XII

Mathematics

Derivative of Some Standard Functions

If f x =| x |...

Question

If f(x) = |x|, then f’(x), where x $\neq$ 0 is equal to

- 1

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\frac{| x |}{x}

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Solution

The correct option is D $\frac{| x |}{x}$
$∵ f (x) = {\begin{matrix} x, x \geq 0 - x, x < 0 \end{matrix} ∵ f^{'} (x) = ⎧ ⎨ ⎩ \begin{matrix} 1, x > 0, i . e, \frac{| x |}{x}, x > 0 - 1, x > 0, i . e, \frac{| x |}{x}, x > 0 \end{matrix} = \frac{| x |}{x}, x \neq 0$

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If f(x) = |x|, then f’(x), where x ≠ 0 is equal to

The correct option is D |x|x∵f(x)={x,x≥0−x,x<0∵f′(x)=⎧⎨⎩1,x>0,i.e,|x|x,x>0−1,x>0,i.e,|x|x,x>0=|x|x,x≠0

If f(x) = |x|, then f’(x), where x $\neq$ 0 is equal to

The correct option is D $\frac{| x |}{x}$
$∵ f (x) = {\begin{matrix} x, x \geq 0 - x, x < 0 \end{matrix} ∵ f^{'} (x) = ⎧ ⎨ ⎩ \begin{matrix} 1, x > 0, i . e, \frac{| x |}{x}, x > 0 - 1, x > 0, i . e, \frac{| x |}{x}, x > 0 \end{matrix} = \frac{| x |}{x}, x \neq 0$