Explore BrainMass

Explore BrainMass

    Using Derivatives to Find Tangent Line and Rate of Change

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    Please see the attached file for correctly formatted equations.

    (3) Find the equation of the line tangent to g(x) = -6x + 64sqrt(x) at x = 16.

    (4) Find the average rate of change of h(x) = -3x^4 + 14x^2 + 22x from x = -3 to x = 5.

    © BrainMass Inc. brainmass.com March 5, 2021, 12:00 am ad1c9bdddf
    https://brainmass.com/math/derivatives/derivatives-find-tangent-line-rate-change-474921

    Attachments

    Solution Preview

    Find the slope of the tangent line by finding the derivative of g(x) and plugging in x = 16:

    Original: g(x) = -6x + 64x^(1/4)

    Derivative: g'(x) = -6 + (1/4)(64)x^(1/4 - 1)

    g'(x) = -6 + 16x^(-3/4)

    Plug in 16: g'(16) = -6 + 16(16)^(-3/4)

    g'(16) = -6 + 16(1/8)

    g'(16) ...

    Solution Summary

    In this solution we show how to use derivatives to solve for the tangent line and rate of change.

    $2.49

    ADVERTISEMENT