Find the absolute maximum value of f(x) = -x^2 + 4x + 1 on the closed interval [0, 3].
Answer and explanation
Correct answer: A. 5
- Step 1: Find critical points: f'(x) = -2x + 4 = 0 gives x = 2, which lies in [0, 3].
- Step 2: Evaluate at critical point and endpoints: f(0) = 1, f(2) = -(4) + 8 + 1 = 5, f(3) = -(9) + 12 + 1 = 4. The maximum is 5.
Answer
5.
Why not the others: '4' is the endpoint value at x=3; '1' is the endpoint value at x=0; '3' is the value of the independent variable at the right boundary.
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