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COMEDK2023Morning ShiftMathematicsApplication of DerivativesActual

Let f(x)=a+(x-4)^ 4 9 , then minima of f(x) is

Options

  1. Aa
  2. Ba - 4
  3. CNone of these
  4. D4

Correct answer

A. a

Step-by-step solution

The function is given by f(x) = a + (x - 4)^ 4 9 . The term (x - 4)^ 4 9 can be written as [9] (x - 4)^4 . Since the exponent 4 9 has an even numerator, the expression (x - 4)^4 is always non-negative for all real x . The minimum value of (x - 4)^4 is 0 , which occurs at x = 4 . Consequently, the minimum value of (x - 4)^ 4 9 is 0^ 4 9 = 0 . Therefore, the minimum value of f(x) = a + (x - 4)^ 4 9 is a + 0 = a . Answer: a

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