2 questions

[Plugga]

I need help with these two questions.


What are the greastest and least values of the Function:

f(x) = (2x-1)(1-x) for 0 =< x =< 1



and



Find the area bounded by the curve y = x^2 + 2x - 3 and the x axis for -4 =< x =< -1

Can you please show all working so I can understand them.

[Evil_Giraffe]

What are the greastest and least values of the Function:
f(x) = (2x-1)(1-x) for 0 =< x =< 1
at x=0, f=-1
at x=1, f=0
since f is continuous and differentiable between 0 and 1 we can find if there are any pointsbetween 0 and 1 that are greater or less by looking at the gradient function, and finding where the gradient is zero and checking those points. We do that so we find all the local maxima (points that are greater than the surrounding values) and minima (points that are less than the surrounding points).
differentiating gives d(2x² + 3x + 1)/dx = 4x + 3
so to find points of zero gradient we solve 4x + 3 = 0
This has no solutions between 0 and 1, so the end points are the greatest and least values.

Find the area bounded by the curve y = x^2 + 2x - 3 and the x axis for -4 =< x =< -1
_-4^-1Sy.dx = [x³/3 + x² - 3x]_-4^-1 = -3
Okay, it's been a while since I did any calculus so don't flame me if it's not quite right.
Hope there was enough working shown.

[Plugga]

Thanks for that, I forgot it and needed to know it for a test that I am going to in about 1 hour