Differentiation and its Application: The function f(x)=sin^4x+cos^4x increases if | IIT-JEE 1999

IIT-JEE 1999Question 1

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

Differentiation and its Application

$0<x<\pi/8$$\pi/4<x<3\pi/8$✓ Correct answer$3\pi/8<x<5\pi/8$$5\pi/8<x<3\pi/4$

Solution

Concept. Write $f$ in terms of $\cos4x$. Formulas used. (1) $\sin^4x+\cos^4x=1-\frac12\sin^22x=\frac34+\frac14\cos4x$Step 1 - Derivative. By (1), $f'(x)=-\sin4x$. Step 2 - Sign. $f'>0$ when $\pi<4x<2\pi$, i.e. $\frac\pi4<x<\frac\pi2$. Step 3 - Option. $\left(\frac\pi4,\frac{3\pi}{8}\right)$ lies inside it. Answer: (B)

Differentiation and its Application - JEE Mathematics question (IIT-JEE 1999)

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