The question statement indicates that the area will be a maximum, but in my attempt you can see that I have arrived at a positive value of 6, suggesting a minimum. I think this has something to do with how I've applied the modulus when calculating the area of the triangle. Specifically, I 'probably' can't define as either or . Furthermore, as you can see, my final answer does not match that of the text book. However, I've been told that my answer is correct, so long as the value expressed is a maximum. Can anyone help me out?
Q. The given diagram (see attachment) shows part of the graph of . p(x, y) is a point on the curve and . bp is perpendicular to ab. (i) Express the coordinates of p in terms of x only, (ii) Find the value of x, if the area of the is a maximum &, hence, find the maximum area.
Attempt: (i) If , then
(ii) From the diagram, we can infer that .
Area of :
Subbing in the vertices of the triangle:
Find derivative to determine value of x: or
Second derivative determines maximum/ minimum area: , where area is a minimum when
Ans.: (From text book): x = 2, Area = 8