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Critical Numbers of Asymptotes

(1) Given function: f(x) = (x^2)*[e^(12x)]
(a) Find its horizontal asymptotes.
(b) Find its critical numbers.
(c) Find its inflection points.

(2) Given function: f(x) = (x^3) / [(x^2) - 16]
(a) Find its critical numbers.
(b) Find its inflection points.

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Solution Preview

Please see the attached file.

(1) Given function: f(x) = (x^2)*[e^(12x)]
(a) Find its horizontal asymptotes.

but
So, y=0 is the only horizontal asymptote

(b) Find its critical numbers.
Since , let f'(x)=0, we get
...

Solution Summary

This shows how to find critical numbers and inflection points of given functions. The critical numbers and inflection on points are determined.

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