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CUET · MATHS · PYQ PAPER 2025

The maximum value of the function f(x) = \(x^2\) (60 - x) in [20, 80] is:

  1. A 16000
  2. B 32000
  3. C 64000
  4. D 128000
Verified Solution

Answer & Solution

Correct Answer

(B) 32000

Step-by-step Solution

Detailed explanation

\(f(x) = 60x^2 - x^3\) \(f'(x) = 120x - 3x^2 = 3x(40 - x)\) \(f'(x) = 0 \implies x = 0, x = 40\) Evaluate \(f(x)\) at \(x = 20, 40, 80\): \(f(20) = (20)^2 (60 - 20) = 400 \times 40 = 16000\) \(f(40) = (40)^2 (60 - 40) = 1600 \times 20 = 32000\)…