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# Finding points on a curve with the equation?

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1. I have the equation y=4x^3-2x, and I don't understand how to find its points Do you have to differentiate?
2. No. Just to plot the curve we know we have a positive cubic.

There is no constant term and so we know the y-intercept is zero. It also factorises to 2x(2x^2-1) and so we know again there is a root at x=0 and the roots of 2x^2-1. These are x= plus or minus root 0.5= plus or minus 0.71.

So we have a positive cubic (low left to high on the right), it goes through the origin and there are roots / x-axis crossing point at +.71 and -0.71.

This is enough to sketch the graph.

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Updated: April 26, 2016
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