Explore BrainMass

Explore BrainMass

    Tangent line

    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!

    Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points.

    The function to define is

    F(x)=2x^3-4x^2+3x-5

    The possible tangent lines are:
    y= x-5

    y= 2x-5

    y= 3x-5

    a) what is/are the zero(es) for this function? In other words, what is the solution for:
    f(x)= 0

    b) what axes values (x- and y- ranges) are appropriate for this graph?

    c) when plotting each linear function with f(x), which line appears to be tangent to the curve at the point

    1) (0,-5)

    2) How about at (1,-4)

    D) What are thederivatives f'(0) and f'(1), and how do they relate to the slopes of the tangent lines to these points?

    E) Find a function for the normal line to the curve at the point (0,-5).

    © BrainMass Inc. brainmass.com March 4, 2021, 9:08 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/tangent-line-problem-219567

    Attachments

    Solution Preview

    The solution is attached below. If you have any question, please let me know. Thank you.

    Explore the following function. You are to decide which of threee lines given are tangent to the graph of f(x) at given points.

    The function to define is

    F(x)=2x^3-4x^2+3x-5
    F'(x) = 6x2 - 8x + 3
    The possible tangent lines are:
    y= x-5
    y= 2x-5
    y= 3x-5

    a) what is/are ...

    Solution Summary

    This provides an example of working through a specified process to find tangent line for a function.

    $2.49

    ADVERTISEMENT