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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES5 Marks
Question
Find the absolute maximum and absolute minimum values of the function f given by $\text{f(x)} = \sin^{2}\text{x} - \cos\text{x , x}\in [0, \pi].$
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Answer

$\text{f(x)} = \sin^{2}\text{x} - \cos\text{x}$
$\text{f}\ '\text{(x) }= \sin\text{x}(2\cos \text{x + 1})$
$\text{f'(x)} = 0\Rightarrow \sin\text{x = 0 and 2}\cos\text{x + 1 = 0} \Rightarrow \text{x = 0, }2\frac{\pi}{3}, \pi$
$\text{f(0)} = -1. \text{f} \bigg(\frac{2\pi}{3}\bigg) = \frac{5}{4}, \text{f}(\pi) = 1$
Absolute maximum value is $\frac{5}{4}$
Absolute minimum value is $-1$

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