The function has a local maximum at the point:

Answer and explanation

Correct answer: A.

  1. Step 1: , so stationary points are at and .
  2. Step 2: The gradient is positive for , negative for and positive for , so is a local maximum.
  3. Step 3: , giving .
Answer
.
Why not the others: is the local minimum; and do not lie on the curve.

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