# 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.

https://brainmass.com/math/synthetic-geometry/critical-numbers-asymptotes-57085

#### Solution Preview

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(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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