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Theorems for Differentiability

In [0, 1] Lag...

Question

In [0, 1] Lagrange's mean value theorem is applicable to

f (x) = ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{1}{2} - x, x < \frac{1}{2} {(\frac{1}{2} - x)}^{2} x \geq \frac{1}{2} \end{matrix}

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f (x) = {\begin{matrix} \frac{s i n x}{x}, x \neq 0 1, x = 0 \end{matrix}

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f(x)=x|x|

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f(x)=|x|

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Solution

The correct option is B $f (x) = {\begin{matrix} \frac{s i n x}{x}, x \neq 0 1, x = 0 \end{matrix}$

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