Posted by Rachal on Wednesday, May 18, 2011 at 5:35am.
The polynomial function is defined by f(x)=4x^4+2x^38x^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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