Question 254427: Find the least value of the polynomial p(x) = x^4 - 4x^3 + 6x^2 - 4x + 6.
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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.
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_poly_maxmin.xml
at x = 1.2, y =
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Find the least value of the polynomial p(x) = x^4 - 4x^3 + 6x^2 - 4x + 6
p'(x) = 4x^3 - 12x^2 + 12x - 4
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Using graphs, or Excel or trial and error, the p' has only one zero, at x = 1
--> the minimum of p(x) is at x = 1, and is p(1) = 5.
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