easy composite

Pre-College Issues High School Life
1

<p>I have to do a calculus project and I need to find a function with 3 critical points, 1 inflection point that´s a composite, like sin(8x). I did have one, (-2x^3 +6x^2)e^2/3x but it seemed to complicated (we have to find all relative mins/maxs, find area under curve, revolve to make a solid and find the volume, so lots of differentiating and integrating. I'm having trouble finding a relatively easy one, like sin(8x). My friend is using that one. </p>

<p>So here's my question: What exactly is an inflection point? I seem to know how to find it without knowing really what it is. I need to look at the graph on my calculator to see if the function will fit the requirements of the projects. Of course, if a few of you nerdy folks want to find a function I can use, I won't protest ;)</p>

<p>Please keep on topic</p>

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<p>inflection point is where the curve changes sign (positive to negative etc., or in other words, changes concavity). It's also the point when the second derivative equals zero or is undefined.</p>

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<p>

It is the point at which the second derivative of the function changes sign, not the function itself. On the function the tangents go from lying above the curve to below or vice versa.
Another way to find an inflection point is to take the graph of the first derivative and locate the minima and maxima.
A function with three critical points and one pt of inflection is the derivative of arcsec x:
[abs(x)(sqrt(x^2-1))]^-1.</p>

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<p>hey, i said in other words concavity....thats gotta count for something</p>

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<p>muchas gracias :p</p>