State all the 0’s and coordinates of the relative maximum and minimum points to the nearest hundredth.

Question

State all the 0’s and coordinates of the relative maximum and minimum points to the nearest hundredth.

x^4 - 2x^3 + x^2 - 2x + 1

Answer 1

This is an onerous question unless you are permitted to use a graphing calculator.

My graphing calculator gives roots of 1.88 and .53 and 2 complex roots.

The single minimum point occurs at approximately x=1.5 and the minimum is approximately -1.5

Without a graphing calculator you could make a rough graph by hand and use Newton' method with first guess of x=2 or you could use Horner's method for irrational roots with the same first guess.