posted by Rachal on .
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.
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)