Question 254427
I couldn't find any formulas that would let you find the minimum of that equation.


I graphed it instead and saw that the minimum point looks like it is at x = 1.


{{{graph(600,600,-5,5,-1,8,x^4 - 4*x^3 + 6*x^2 - 4*x + 6)}}}


I took 2 points before and after 1 to test this out.


I chose x = .8 and x = 1.2


at x = .8, y = 5.0016


at x = 1.2, y = 5.0016


this kind of confirms that the axis of symmetry is at x = 1.


you can try other points like .9 and 1.1, and .7 and 1.3.


I suspect the minimum point is at x = 1.


I checked out a website that talked about minimum and maximum points of a polynomial, but I couldn't find anything in there that showed how it could be done other than graphically.


click here for that.


<a href = "http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_maxmin.xml" target = "_blank">http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_maxmin.xml</a>





at x = 1.2, y =