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MHT CET202520 Apr 2025Evening ShiftMathematicsApplication of DerivativesActual

If the curve y=a x^2-6 x+b passes through (0,4) and has its tangent parallel to the x -axis at x= 3 2 , then the value of a and b respectively are

Options

  1. A-2,-4
  2. B2, 4
  3. C-2,4
  4. D2,-4

Correct answer

B. 2, 4

Step-by-step solution

The curve y=ax^2-6x+b passes through the point (0,4) , so substituting gives 4=a(0)^2-6(0)+b , which simplifies to b=4 . Since the tangent is parallel to the x-axis at x= 3 2 , the derivative dy dx =2ax-6 must be zero at that point. Setting 2a 3 2 -6=0 yields 3a-6=0 , so a=2 . The values are therefore a=2 and b=4 , corresponding to option B .

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