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?

Many thanks.

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

Area:

**Ans.:** (From text book): x = 2, Area = 8