For the polynomial function ƒ(x) = −0.02x4 + .36x2 − 1.62, find all local and global extrema

Dy/dx=-.08x^3+.72x

d2y/dx2=-.24x^2+.72

.08x(9-x^2) so we have extrema at x=-3,0,3

d2y/dx2 (-3)=-1.44, (0)=.72, (3)=-1.44

So you have two global maximums at (±3,0)

We have a local minimum at (0,-1.62)

There are no global minimums as the function decreases without bound as x approaches ±oo

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