Pre calc question

Question

Graph x⁴-5x³+2x²+x-3 Identify the  x-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. Round to the nearest hundredth, if necessary.

Answer 1

Examining the graph on desmos....

x-intercepts at x=-0.766 and x=4.543...

apparently there are two imaginary/complex solutions

local min (-0.156, -3.088) = (xmin,ymin)

local max (0.468, -2.558) = (xMax, yMax)

Decreasing on (-infinity, xMin) U (xMax,3.438)

increase on (xmin,xMax) U ( 3.438,infinity)