If the function f(x)= -x 2 + defined on [- 3 , 3 ] is: - Vidyadip

MCQ

If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:

✓
Increasing.
B
Decreasing.
C
Constant.
D
None of these.

✓

Answer

Correct option: A.

Increasing.

$\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$
$\therefore\ \text{f}'(\text{x})=\frac{-1}{2}+\cos\text{x}$
$\Rightarrow\text{f}'(\text{x})\geq0,\forall\ \text{x}\in\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$
$\Big[\because\ \text{for }\text{x}\in\Big[\frac{-\pi}{3},\frac{-\pi}{3}\Big],\cos\geq\frac{1}{2}\Big]$
Hence, the given function is increasing.

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