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QUESTION

# 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.

y= 1/10x^5 +1/2x^4 -3/10 y'=1/2x^4+ 2x^3 y''=2x^3+6x^2

We set our second derivative to 0: y''=x^2(2x+6)=0

And we can find our inflection points through these equations:

• x^2=0
• 2x+6=0

Our Inflection Points are then at x= 0, and x=-3