Question

Calculus help

Find the relative extrema of the function
f(x) = x^4 - 32x^2 + 3

I've worked this out on the calculator, but I am unsure how to do on pen and paper. I tried completing the square, but it doesn't seem to come out right.

Relative maximum at (0, 3); relative minima at (4, -253), (-4, -253)

Answer 1

take the derivative

Answer 2

3x^3-64x
This doesn't factor evenly

Answer 3

\[f \prime \left( x \right)=4x^3-64x\]
\[f \prime \left( x \right)=0~gives~4x^3-64x=0\]
4x(x^2-16)=0
x=0,-4,4

Answer 4

find \[f \prime \prime \left( x \right) ~all~three~ points~for~maxima~and~minima.\]

Answer 5

Wow, I missed that one, Thanks

Answer 6

nope this helps too.