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MHT CET202618 April 2026Evening ShiftMathematicsApplication of DerivativesActual

If the function f(x) = ax^2 + bx + x satisfies all the conditions of Rolle's theorem on [0, ] and the slope of the tangent to the curve y = f(x) at x = 4 is zero, then a - b =

Options

  1. A2 (1- )
  2. B2 (2+ )
  3. C2 ( -1)
  4. D2 ( +1)

Correct answer

D. 2 ( +1)

Step-by-step solution

Since f(x) satisfies Rolle's theorem on [0, ] , we have f(0) = f( ) . a(0)^2 + b(0) + 0 = a ^2 + b + 0 = a ^2 + b b = -a The slope of the tangent at x = 4 is zero, so f' ( 4 ) = 0 . f'(x) = 2ax + b + x f' ( 4 ) = 2a ( 4 ) + b + ( 4 ) = 0 a 2 + b + 1 2 = 0 Substituting b = -a : a 2 - a + 1 2 = 0 - a 2 + 1 2 = 0 a = 2 Using b = -a , we get b = - 2 . Therefore, a - b = 2 - (- 2 ) = 2 ( +1) . Answer: 2 ( +1)

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