Posted by **Rachal** on Wednesday, May 18, 2011 at 5:35am.

The polynomial function is defined by f(x)=4x^4+2x^3-8x^-5x+2.

Use a calculator to find all the points (x,f(x)) where there is a local maximum.

Round to the nearest hundredth.

- Algebra -
**Reiny**, Wednesday, May 18, 2011 at 8:09am
f '(x) = 16x^3 + 6x^2 - 16x - 5 , ( I assumed the second last term was -8x^2 )

16x^3 + 6x^2 - 16x - 5 = 0

zeros for this equation exist at

appr. -1,1 and -.3

f ''(x) = 48x^2+ 12x - 16

both f ''(1) and f ''(-1) > 0

but f ''(-.3) < 0

so when x = -.3 (appr), we have a local maximum

I will let you find f(-.3)

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