COMEDK · Maths · 27. Application of Derivatives
\(\text { If } f(x)=\dfrac{a \sin x+b \cos x}{c \sin x+d \cos x} \text { is decreasing for all } x \text {, then }\)
- A \(a b-c d>0\)
- B \(a d-b c<0\)
- C \(a d-b c>0\)
- D \(a b-c d<0\)
Answer & Solution
Correct Answer
(B) \(a d-b c<0\)
Step-by-step Solution
Detailed explanation
Given \(f(x) = \dfrac{a \sin x + b \cos x}{c \sin x + d \cos x}\). To determine the condition for \(f(x)\) to be decreasing, we find the derivative \(f'(x)\) using the quotient rule \(\left( \dfrac{u}{v} \right)' = \dfrac{u'v - uv'}{v^2}\). Let \(u = a \sin x + b \cos x\) and…
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