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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
Assertion (A) : Both $\sin x$ and $\cos x$ are decreasing functions in $\left(\frac{\pi}{2}, \pi\right)$.
Reason (R): If a differentiable function decreases in $(a, b)$, then its derivative also decreases in $(a, b)$.
  • A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
  • B
    Both (A) and (R) are true but (R) is not the correct explanation of (A).
  • C
    (A) is true but (R) is false.
  • D
    (A) is false but (R) is true.
✓

Answer

(c) : We know that, $\sin x$ and $\cos x$ decrease in $\frac{\pi}{2}$ < x < $\pi$, so assertion is correct.
Image

Reason is wrong which is clear from the graph that $f(x)$ is differentiable in $(a, b)$.
Also, $a < x_1 < x_2 < b$
But $f^{\prime}\left(x_1\right)=\tan \phi_1<\tan \phi_2=f^{\prime}\left(x_2\right)$
$\Rightarrow$ Derivative is increasing.

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