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KCET2026MathematicsApplication of Derivatives

A YouTube short video is getting viral according to f(t) = -2t^3 + 3t^2 + 5 . At what time does the video get maximum number of shares? ( t is in hours)

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

Given the function f(t) = -2t^3 + 3t^2 + 5 . Differentiating with respect to t , we get: f'(t) = -6t^2 + 6t For maximum or minimum, f'(t) = 0 : -6t^2 + 6t = 0 -6t(t - 1) = 0 This gives t = 0 or t = 1 . Now, finding the second derivative: f''(t) = -12t + 6 At t = 0 , f''(0) = 6 > 0 , which corresponds to a local minimum. At t = 1 , f''(1) = -12(1) + 6 = -6 Thus, the video gets the maximum number of shares at t = 1 . Answer: 1

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