SATHEE: Application of Derivatives 2 Question 13

Application of Derivatives 2 Question 13

####13. The function $f (x) = \sin^{4} x + \cos^{4} x$ increases, if

(a) $0 < x < \frac{π}{8}$

(b) $\frac{π}{4} < x < \frac{3 π}{8}$

(d) $\frac{5 π}{8} < x < \frac{3 π}{4}$

$(1999, 2 M)$

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Answer:

(c)

Solution:

Given, $f (x) = \sin^{4} x + \cos^{4} x$

On differentiating w.r.t. $x$ , we get

$\begin{aligned} f^{'} (x) & = 4 \sin^{3} x \cos x - 4 \cos^{3} x \sin x \\ = 4 \sin x \cos x (\sin^{2} x - \cos^{2} x) \\ = 2 \sin 2 x (- \cos 2 x) \\ = - \sin 4 x \end{aligned}$

Now, $f^{'} (x) > 0$ , if $\sin 4 x < 0$

$\begin{array}{ll} \Rightarrow & π < 4 x < 2 π \\ \Rightarrow & \frac{π}{4} < x < \frac{π}{2} \end{array}$

$\Rightarrow$ Option (a) is not proper subset of Eq. (i), so it is not correct.

Now,

$\frac{π}{4} < x < \frac{3 π}{8}$

Since, option (b) is the proper subset of Eq. (i), so it is correct.

Application of Derivatives 2 Question 13

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Application of Derivatives 2 Question 13

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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