Wednesday, December 15, 2010

How to calculate the vertex of the curve y=2x^2-4x+4 using derivatives?

The vertex of the given parabola represents the extreme
point of the function.


To determine the extreme point,
we'll have to calculate the critical value of the
function.


The critical value of the function is the zero of
the 1st derivative.


y' =
4x-4


We'll cancel the 1st
derivative:


4x-4 = 0


4x = 4
=> x = 1


f(1) = 2 - 4 +
4


f(1) = 2


The
vertex of the parabola is the minimum point of the function and it's coordinates are
(1,2).

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