Draw a picture of this situation. Recognize that the base of the triangle is p-2 and that the height is -x^2+8p-12. Thus, the area of this triangle is
(b)(h) (p-2)(-x^2+8p-12)
A = ---------- = -----------------------------
2 2
Differentiate this function. Set the result = to 0. Solve for the critical values 2 and 14/3. Only p=14/3 makes sense, since the area of the triangle would be zero if you were to choose p=2.
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