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COMEDK20269 May 2026Morning ShiftMathematicsApplication of DerivativesActual

If the function f(x) = x^4 - 31x^2 + ax + 5 has a turning point at x = 1 , then the value of ' a ' is ___ and the function attains a ___ at x = 1

Options

  1. Aa = -50 , local maxima
  2. Ba = 58 , local maxima
  3. Ca = 50 , local minima
  4. Da = 58 , local minima

Correct answer

B. a = 58 , local maxima

Step-by-step solution

Given f(x) = x^4 - 31x^2 + ax + 5 Differentiating with respect to x , we get: f'(x) = 4x^3 - 62x + a Since f(x) has a turning point at x = 1 , f'(1) = 0 4(1)^3 - 62(1) + a = 0 a = 58 Now, finding the second derivative: f''(x) = 12x^2 - 62 At x = 1 , f''(1) = 12(1)^2 - 62 = -50 Since f''(1) Answer: a = 58 , local maxima

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