CUET · MATHS · PYQ PAPER 2025
The total cost function is given by \(C(x)=\frac{1}{3} x^3-5 x^2+30 x-15\) and selling price per unit is Rs. 6. The profit is maximum if the value of x is:
- A x = 4
- B x = 6
- C x = 5
- D x = 10
Answer & Solution
Correct Answer
(B) x = 6
Step-by-step Solution
Detailed explanation
\(R(x) = 6x\) \(P(x) = R(x) - C(x) = 6x - (\frac{1}{3} x^3-5 x^2+30 x-15) = -\frac{1}{3} x^3 + 5 x^2 - 24 x + 15\) \(P'(x) = -x^2 + 10x - 24\) \(P'(x) = 0 \Rightarrow -x^2 + 10x - 24 = 0 \Rightarrow x^2 - 10x + 24 = 0 \Rightarrow (x-4)(x-6) = 0\) \(x = 4\) or \(x = 6\)…
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