What is the local maximum and or miminum of the function f(x)=2x^2+2x^2-4xf(x)=2x2+2x24x?

1 Answer
Feb 15, 2015

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f(x) = 2x^2 + 2x^2 - 4xf(x)=2x2+2x24x
is equivalent to
f(x) = 4x^2 - 4xf(x)=4x24x

f'(x) = 8x - 4
At the local maximum/minimum
f'(x) = 0
that is
8x - 4 = 0 rarr x = 1/2#

f( 1/2 ) = -1
Since the coefficient of x^2 is positive
this is a local minimum
which occurs at (x,f(x)) = ( 1/2, -1)