Calculus, help please!!!?

Question

It's about the application of Explicit Differentiation!!!
(Solving Maxima and Minima Pronlems)

Find the dimensions of a right circular cylinder of grestest volume which can be inscribed in a right circular cone with radius of 5in. and a height of 12in,

Answer 1

Find a function that represents the cylinder volume with respect to height (for a varying radius).

I did this using Microsoft Excel, charting cylinder volume versus height, then using the trendline function (linear regression) for a 3rd-degree polynomial fit. The R^2 value was 1, so the function was accurate (I even checked it by plotting it). You can use any linear regression tecnique you choose.

Once you plot your function: cylinder volume (Y) versus height (X), you can plainly see where the maximum volume lies, and what the height is.

To obtain an exact maxima, differentiate the function and set it equal to zero (slope = 0 at a minima or maxima), solve for X (the height @ max vol.), then plug that X value back into the origial function to find the volume. NOTE: in this case the differentiated function will be a quadratic, so there will be 2 values for Y. Only one of them will make sense -- that's the correct height.

If you try this and edit your question, I can check your work for correctness.

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