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Standard XII

Mathematics

Chain Rule of Differentiation

Let fx = x2...

Question

Let $f (x) = x^{2} | x |$ , then the number of values of $x$ , where $f (x)$ is three times differentiable is

Infinite

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Solution

The correct option is D Infinite
$f (x) = x^{3}$ for $x \geq 0$
$f (x) = - x^{3}$ for $x < 0$
$f^{'''} (x) = 6$ for $x \geq 0$
$f^{'''} (x) = - 6$ for $x < 0$
Therefore, $f (x)$ is differentiable at all $x$ except at $0$
Hence, answer is A

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Let f(x)=x2|x|, then the number of values of x, where f(x) is three times differentiable is

The correct option is D Infinitef(x)=x3 for x≥0f(x)=−x3 for x<0f′′′(x)=6 for x≥0f′′′(x)=−6 for x<0Therefore, f(x) is differentiable at all x except at 0Hence, answer is A

Let $f (x) = x^{2} | x |$ , then the number of values of $x$ , where $f (x)$ is three times differentiable is

The correct option is D Infinite
$f (x) = x^{3}$ for $x \geq 0$
$f (x) = - x^{3}$ for $x < 0$
$f^{'''} (x) = 6$ for $x \geq 0$
$f^{'''} (x) = - 6$ for $x < 0$
Therefore, $f (x)$ is differentiable at all $x$ except at $0$
Hence, answer is A