AP EAMCET · Maths · Application of Derivatives
If \(x+y=k, x>0, y>0\), then \(x^2+y^2\) is minimum, if
- A \(x>y\)
- B \(x < y\)
- C \(x=y\)
- D \(x=2 y\)
Answer & Solution
Correct Answer
(C) \(x=y\)
Step-by-step Solution
Detailed explanation
\[ \begin{gathered} x+y=k \\ \Rightarrow y=k-x, x>0, y>0 \end{gathered} \] Consider \[ \begin{aligned} & A=x^2+y^2=x^2+(k-x)^2=2 x^2-2 k x+k^2 \\ & \frac{d A}{d x}=4 x-2 k=0 \Rightarrow x=\frac{k}{2} \\ & \frac{d^2 A}{d x^2}=4>0 \end{aligned} \] \(\therefore\) At…
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