Explore BrainMass

Explore BrainMass

    Maximum and minimum values

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

    Given: y = f(x) = 3x4 + 4x3

    Find:
    A. All critical points
    B. Max - Min Values
    C. Inflection points
    D. Where is f(x) concave up
    E. Where is f(x) concave down
    F. X and Y intercepts
    G. Where f(x) is increasing
    H. Where f(x) is decreasing
    I. Sketch the curve label

    © BrainMass Inc. brainmass.com February 24, 2021, 2:27 pm ad1c9bdddf
    https://brainmass.com/math/optimization/maximum-minimum-values-22031

    Solution Preview

    f(x) = 3x^4 + 4x^3
    => f'(x) = 12x^3 + 12x^2 = 12x^2(x+1)
    => f''(x) = 36x^2 + 24x
    => f'''(x) = 72x + 24
    => f''''(x) = 72
    A.)
    For critical points:
    f'(x) = 0 => 12x^2(x+1) = 0
    => x = 0, -1 --Answer

    B.)
    =>f''(0) = 0 : Neither max nor min
    => f'''(0) =
    f''(-1) = 36 - 24 = 12: minima

    f(infinity) = infinity
    f(-infinity) ...

    Solution Summary

    This shows how to find critical points and concavity.

    $2.19

    ADVERTISEMENT