What is the x-coordinate of the point of inflection on the graph of ##y=1/10x^(5)+1/2X^(4)-3/10##?
We find the Inflection Points of ##y## by finding the second derivative of the function (y”), and the x-values at which y” equals 0.
We look for the zeroes because at those points the concavity (or the direction in which the slope of the function ##f(x)## is trending) has leveled off; it is at these points that the concavity is most likely to turn from positive to negative, or vice-versa.
Just as background, Math is Fun offers notes on inflection points.
We set our second derivative to 0: ##y”=x^2(2x+6)=0##
And we can find our inflection points through these equations:
Our Inflection Points are then at ##x= 0, and x=-3##
