The function f(x) = sin^4 x + cos^4 x is incr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = \sin^4 x + \cos^4 x$. We can rewrite this as $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\sin x \cos x)^

Vedclass · Accepted Answer

$\frac{\pi}{4} < x < \frac{\pi}{2}$

Vedclass · Answer

(B) Given $f(x) = \sin^4 x + \cos^4 x$. We can rewrite this as $f(x) = (\sin^2 x + \cos^2 x)^2 - 2\sin^2 x \cos^2 x = 1 - \frac{1}{2}(2\sin x \cos x)^2 = 1 - \frac{1}{2}\sin^2 2x$. Differentiating with respect to $x$,we get $f'(x) = -\frac{1}{2} \cdot 2\sin 2x \cdot \cos 2x \cdot 2 = -2\sin 2x \cos 2x = -\sin 4x$. For $f(x)$ to be increasing,$f'(x) > 0$,so $-\sin 4x > 0$,which implies $\sin 4x The sine function is negative in the third and fourth quadrants,so $\pi Dividing by $4$,we get $\frac{\pi}{4} < x < \frac{\pi}{2}$.

The function $f(x) = \sin^4 x + \cos^4 x$ is increasing in

Similar Questions

Let $f(x) = x^3 + bx^2 + cx + d$ where $0 < b^2 < c$. Then $f(x)$:

If $f(x) = x^3 - 6x^2 + 9x + 3$ is a monotonically decreasing function,then $x$ lies in:

The length of the longest interval,in which the function $f(x) = 3\sin x - 4\sin^3 x$ is increasing,is

In which interval does the function $f(x) = 2x^2 - \log |x|$ $(x \neq 0)$ monotonically increase?

The function $f(x) = \frac{4x^3 - 3x^2}{6} - 2 \sin x + (2x - 1) \cos x$:

Vedclass Test Series

Exam Paper Generator

Online Exam Module