(C) The function is defined as $f(x) = |x|$.For $x 0$,$f(x) = x$.At $x = 0$,$f(0) = 0$.Since $|x| \geq 0$ for all real $

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$f(x)$ has a minimum at $x = 0$.

(C) The function is defined as $f(x) = |x|$.For $x 0$,$f(x) = x$.At $x = 0$,$f(0) = 0$.Since $|x| \geq 0$ for all real $x$,the value $f(0) = 0$ is the smallest possible value of the function.Therefore,$f(x)$ has a global minimum at $x = 0$.Note that $f'(0)$ does not exist because the left-hand derivative is $-1$ and the right-hand derivative is $1$.

Class 12 Mathematics Continuity and Differentiation Differentiability

Easy

Let $f(x) = |x|$. Then which of the following is true?

A
$f'(0) = 0$
B
$f(x)$ has a maximum at $x = 0$.
C
$f(x)$ has a minimum at $x = 0$.
D
$f(x)$ has both a maximum and a minimum.

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Class 12

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Continuity and Differentiation

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Differentiability

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Let $f:R \to R$ be a function defined by $f(x) = \max \,(x, x^3).$ The set of all points where $f(x)$ is not differentiable is

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Which one of the following functions is continuous everywhere in its domain but has at least one point where it is not differentiable?

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The number of points at which the function,$f(x) = |x - 0.5| + |x - 1| + \tan x$ does not have a derivative in the interval $(0, 2)$ is :

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Let $f(x) = |x|$. Then which of the following is true?

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