JEE PYQ: Application Of Derivatives Question 36
Question 36 - 2020 (05 Sep Shift 1)
If the minimum and the maximum values of the function $f : \left[\frac{\pi}{4}, \frac{\pi}{2}\right] \to \mathbb{R}$, defined by
$$f(\theta) = \begin{vmatrix} -\sin^2\theta & -1-\sin^2\theta & 1 \ -\cos^2\theta & -1-\cos^2\theta & 1 \ 12 & 10 & -2 \end{vmatrix}$$
are $m$ and $M$ respectively, then the ordered pair $(m, M)$ is equal to:
(1) $(0, 2\sqrt{2})$
(2) $(-4, 0)$
(3) $(-4, 4)$
(4) $(0, 4)$
Show Answer
Answer: (2)
Solution
Applying $C_2 \to C_2 - C_1$: $f(\theta) = 4(\cos^2\theta - \sin^2\theta) = 4\cos 2\theta$. For $\theta \in [\frac{\pi}{4}, \frac{\pi}{2}]$: $\cos 2\theta \in [-1, 0]$. So $m = -4$, $M = 0$.
BETA
