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 Question from bailey, a student: Hi there, A right angled triangle OPQ is drawn as shown where O is at (0,0). P is a point on the parabola y = ax – x^2 and Q is on the x-axis. Show that the maximum possible area for the triangle OPQ is (2a^3)/(27) It has been bugging me from the test. Thanks :)

Hi Bailey

I expect the diagram looks something like this. I gave $Q$ the coordinates $(x,0).$

What is the y-coordinate of $P?$ That's the height of the triangle. What is the area of this triangle? Use the calculus you know to find the value of $x$ that maximizes the area. What is the area at for value of $x?$

Penny

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