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musicmar
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Homework Statement
a. The area of a triangle is formed in the first quadrant by the x and y axes and a line through the point (2,1).
i. Write the area of the triangle as a function of x.
ii.Determine the domain of the function.
iii.Is there a maximum and minumum area for some value of x? If so, find the value analytically and graphically.
The Attempt at a Solution
I did part i and ii and only really need help with iii.
For i, I drew a graph of the first quadrant with a point at (2,1) and an arbitrary line through it and both axes. I have attached a graph from paint. I found the slope of the blue line (-1/x-2) and set it equal to the slope of the whole line (-y/x) in order to solve for y in terms of x. Because y= x/(x-2), the area of the triangle is:
A= 1/2 bh
=1/2 xy
= (x^2)/2(x-2)
ii. D: (2,infinity)
iii. I know there must be a maximum and minimum area as x approaches 2 and infinity, but I don't know how to "find the value analytically and graphically".