(A) Given the function $f(x) = \sin x$. To determine the nature of the function,we find its derivative: $f'(x) = \cos x$. Now,we evaluate the derivati

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(A) Given the function $f(x) = \sin x$. To determine the nature of the function,we find its derivative: $f'(x) = \cos x$. Now,we evaluate the derivative at $x = 2\pi / 3$: $f'(2\pi / 3) = \cos(2\pi / 3) = -1/2$. Since $f'(2\pi / 3) Therefore,the function is monotonically decreasing at this point.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Medium

What is the nature of the function $f(x) = \sin x$ at $x = 2\pi / 3$?

A
Monotonically decreasing
B
Monotonically increasing
C
Neither monotonically increasing nor decreasing
D
None of these

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Applications of Derivatives

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Increasing and Decreasing function

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What is the nature of the function $f(x) = \sin x$ at $x = 2\pi / 3$?

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