Question

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

Answer 1

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`f(x) = 2x^2 + 2x^2 - 4x`
is equivalent to
`f(x) = 4x^2 - 4x`

`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)`