TS EAMCET · Maths · Application of Derivatives
The sum of two numbers is 20 . If the product of the square of one number and cube of the other is maximum, then the numbers are :
- A 12,8
- B 3,4
- C 9,12
- D 15,18
Answer & Solution
Correct Answer
(A) 12,8
Step-by-step Solution
Detailed explanation
Let the numbers be \(x, y\). \(\therefore \quad x+y=20 \Rightarrow y=20-x\) Let \(S=x^3(20-x)^2\) On differentiating w.r.t \(x\), we get \(\frac{d S}{d x}=2 x^3(20-x)(-1)+3 x^2(20-x)^2\) For maximum or minimum, put \(\frac{d S}{d x}=0\)…
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