MCQ
Sum of minimum and maximum values of the function $f(x)$ = $cos^{-1}x+ 2cot^{-1}x -2x^3 -4x$ is
- A$-3\pi $
- B$3 + 2\pi$
- ✓$3\pi $
- D$2 - 3\pi$
✓
Answer
Correct option: C.
$3\pi $
c
Domain of $f(\mathrm{x})$ is $[-1,1]$
Domain of $f(\mathrm{x})$ is $[-1,1]$
$f^{\prime}(\mathrm{x})=\frac{-1}{\sqrt{1-\mathrm{x}^{2}}}-\frac{2}{1+\mathrm{x}^{2}}-6 \mathrm{x}^{2}-4<0$
$f(\mathrm{x})$ is decreasing function
$\therefore $ ${\text { Min. value }=0+\frac{\pi}{2}-2-4} $
${\mathrm{m}=\frac{\pi}{2}-6}$
Max value $=\pi+\frac{3 \pi}{2}+2+4$
$M=6+\frac{5 \pi}{2}$
$\mathrm{m}+\mathrm{M}=3 \pi$
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