COMEDK · Maths · 26. Differentiation
Divide 20 into two parts such that the product of one part and the cube of the other is maximum. The two parts are
- A \((12,8)\)
- B \((15,5)\)
- C \((10,10)\)
- D \((2,18)\)
Answer & Solution
Correct Answer
(B) \((15,5)\)
Step-by-step Solution
Detailed explanation
According to question, \(x+y=20 \quad \text{...(i)}\) and \(\quad p=x y^{3}=(20-y) y^{3} \quad\) [by Eq. (i)] \(p=20 y^{3}-y^{4}\) \(\Rightarrow \quad \frac{d p}{d y}=60 y^{2}-4 y^{3}\) \(\Rightarrow \quad \frac{d^{2} p}{d y^{2}}=120 y-12 y^{2}\) Now,…
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