Posted by elley on Tuesday, November 11, 2008 at 7:35pm.
if f(x)=uvw
then
f'(x)=uvw'+ uwv'+ wvu'
I will assume you really meant to write the derivative y' and not the function y although I would have thought the book would ask you to find that derivative.
Wherever that derivative, y', is zero, the curve is horizontal
This is twice at x = 1 and at x =2 and at x = 4
Look at the second derivative to see what happens there.
y'=(x-1)^2 (x^2-6x+8)
so
y" = (x-1)^2(2x-6)+2(x-1)(x^2-6x+8)
now what is y"at x = 1?
y"(1) = Zero, so that is an inflection point
what is y" at x = 2?
y"(2) = -2+0 = -2
That is a maximum because y" is negative
what is y"(4)?
y"(4) = 9(2)+2*3(16-24+8)
y"(4) = 18+0 = 18
so it is Minimum at x = 4
y"
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