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AP EAMCET · Maths · Application of Derivatives

If \(x^2+y^2=25\), then \(\log _5[\max (3 x+4 y)]\) is

  1. A \(2\)
  2. B \(3\)
  3. C \(4\)
  4. D \(5\)
Verified Solution

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…