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

Question

Mathematics

Amara Valenzuela

27 January, 09:40

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

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Answers (1)

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Angelo Boyd · Answer 1

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