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

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(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

$b < 4$

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(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:

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