AP EAMCET · Maths · Application of Derivatives
If \(x^2+y^2=25\), then \(\log _5[\max (3 x+4 y)]\) is
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(A) \(2\)
Step-by-step Solution
Detailed explanation
Given \(x^2+y^2=25\) \(\begin{aligned} & \Rightarrow \quad y=\sqrt{25-x^2} \\ & \text { Let } z=3 x+4 y \\ & \Rightarrow \quad z=3 x+4 \sqrt{25-x^2} \end{aligned}\) Differentiating w.r.t. \(x\), we get \(\frac{d z}{d x}=3+\frac{4}{2 \sqrt{25-x^2}}(-2 x)\) For maxima put…
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3. \pm 2
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