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Anyone can help me with this question? I would so much appreciate for helping me out!

Anyone can help me with this question? I would so much appreciate for helping me out-example-1
User Mannaggia
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1 Answer

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I strongly recommend that you draw this situation. The vertices of the right triangle are (2,0), (p,0) and (p, -p^2+8p-12).

We are to maximize the area of the triangle. To do this, we find the equation for the area (which is based upon the usual b*h/2), differentiate this formula, set the derivative = to 0 and solve for p. I obtained p = 14/3, or 4 2/3 units.

Keep in mind that the correct expression for the base here is p-2. Can you see why? The height is simply the function itself: p(x) = -x^2+8x-12.
Thus, the area of the triangle, in terms of p, is

(p-2)(-p^2+8p-12)
A(p) = ---------------------------
2

Let me know if you need further help with this problem. Good luck!

User Sasindu H
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