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COMEDK20269 May 2026Evening ShiftMathematicsApplication of DerivativesActual

The absolute maximum and minimum values of the function f(x) = x + 3 x in [0, ] are

Options

  1. AMinimum value = 3 , maximum value = 2
  2. BMinimum value = - 3 , maximum value = 2
  3. CMinimum value = - 1 3 , maximum value = 2
  4. DMinimum value = 1 3 , maximum value = 2

Correct answer

B. Minimum value = - 3 , maximum value = 2

Step-by-step solution

Given f(x) = x + 3 x We can rewrite the function as: f(x) = 2 ( 1 2 x + 3 2 x ) = 2 (x + 3 ) For x [0, ] , the angle (x + 3 ) [ 3 , 4 3 ] . The maximum value of (x + 3 ) in this interval is 1 , which occurs at x + 3 = 2 x = 6 . Thus, the absolute maximum value of f(x) is 2 1 = 2 . The minimum value of (x + 3 ) in this interval occurs at the endpoint x + 3 = 4 3 x = . Thus, the absolute minimum value of f(x) is 2 ( 4 3 ) = 2 (- 3 2 ) = - 3 . Alternatively, evaluating the function at the critical point x = 6 and the

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