(A) Given the function $f(x) = x$ defined on the interval $[-1, 1]$.To determine the nature of the function,we find its derivative with respect to $x$

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(A) Given the function $f(x) = x$ defined on the interval $[-1, 1]$.To determine the nature of the function,we find its derivative with respect to $x$:$f'(x) = \frac{d}{dx}(x) = 1$.Since $f'(x) = 1 > 0$ for all $x \in [-1, 1]$,the function $f(x)$ is strictly increasing on the given interval.Therefore,the correct option is $A$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

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If $f(x) = x$,$-1 \le x \le 1$,then the function $f(x)$ is

A
Increasing
B
Decreasing
C
Stationary
D
Discontinuous

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Class 12 Questions

Class 12

Mathematics Questions

Chapter

Applications of Derivatives

Subtopic

Increasing and Decreasing function

In which interval is the function $f(x) = 2x^2 - \ln |x|$ $(x \ne 0)$ monotonically decreasing?

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For what values of $x$ is the function $f(x) = x + \frac{1}{x}, x \neq 0$ strictly increasing?

Medium

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Show that the function $f$ given by $f(x) = \tan^{-1}(\sin x + \cos x), x > 0$ is always an increasing function in $\left(0, \frac{\pi}{4}\right)$.

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$2{x^3} - 6x + 5$ is an increasing function if

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The function $f(x) = x + \frac{1}{x}, (x \neq 0)$ is a non-increasing function in the interval

Easy

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If $f(x) = x$,$-1 \le x \le 1$,then the function $f(x)$ is

Similar Questions

In which interval is the function $f(x) = 2x^2 - \ln |x|$ $(x \ne 0)$ monotonically decreasing?

For what values of $x$ is the function $f(x) = x + \frac{1}{x}, x \neq 0$ strictly increasing?

Show that the function $f$ given by $f(x) = \tan^{-1}(\sin x + \cos x), x > 0$ is always an increasing function in $\left(0, \frac{\pi}{4}\right)$.

$2{x^3} - 6x + 5$ is an increasing function if

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