Explore BrainMass
Share

Explore BrainMass

    Critical Numbers of Asymptotes

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    (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.

    © BrainMass Inc. brainmass.com October 9, 2019, 5:26 pm ad1c9bdddf
    https://brainmass.com/math/synthetic-geometry/critical-numbers-asymptotes-57085

    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.

    $2.19