If f(x) = frac{sin x + b cos x}{sin x + 4 cos | vedclass

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

Question

(B) Let $f(x) = \frac{a \sin x + b \cos x}{c \sin x + d \cos x}$.For $f(x)$ to be a strictly increasing function,its derivative $f'(x)$ must be greate

Vedclass · Accepted Answer

$b < 4$

Vedclass · Answer

(B) Let $f(x) = \frac{a \sin x + b \cos x}{c \sin x + d \cos x}$.For $f(x)$ to be a strictly increasing function,its derivative $f'(x)$ must be greater than $0$.$f'(x) = \frac{(a \cos x - b \sin x)(c \sin x + d \cos x) - (a \sin x + b \cos x)(c \cos x - d \sin x)}{(c \sin x + d \cos x)^2}$.Simplifying the numerator,we get $ad - bc > 0$.In the given function $f(x) = \frac{1 \sin x + b \cos x}{1 \sin x + 4 \cos x}$,we have $a=1, b=b, c=1, d=4$.Applying the condition $ad - bc > 0$:$(1)(4) - (b)(1) > 0$$4 - b > 0$$4 > b$ or $b < 4$.

If $f(x) = \frac{\sin x + b \cos x}{\sin x + 4 \cos x}$ is a strictly increasing function,then:

Similar Questions

In which interval is the function $f(x) = \tan^{-1}(\sin x + \cos x)$ an increasing function?

Let $f(x) = \frac{x}{\sqrt{a^2 + x^2}} - \frac{d - x}{\sqrt{b^2 + (d - x)^2}}$,$x \in R$,where $a, b$ and $d$ are non-zero real constants. Then:

The set of all $x$ for which $\sin x \leq x$ is

The function $f(x) = \tan^{-1}(\sin x + \cos x)$,$x > 0$ is always an increasing function on the interval

For which value of $x$ is the function $f(x) = x^2 - 2x$ decreasing?

Vedclass Test Series

Exam Paper Generator

Online Exam Module