Caculus f'(x)

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For what values of a and b is the line –2x+y=b tangent to the curve y=ax^3 when x=–2?

a= ?
b= ?

Thanks guys!

  • Caculus f'(x) -

    First, you rewrite the equation as:

    -2∙-2 + a∙-2^3

    Next, you solve some of it to get:

    4 + a∙8

    Finally, if you can't figure out what a and b are, you can do what I did above, and try figuring it out. I did not know how to solve to get a and b, but at least you have the things above to help.

  • Calculus f'(x) (Misspelled Subject Name) -

    Oh, and by the way, it is actually Calculus instead of Caculus for the subject name of your problem. I just noticed it.

  • Caculus f'(x) -

    For a if it is 4, you will get the next equation of:

    4 + 4∙8 = b

    Finally, you solve, and you get:

    36 as your answer for b.

    So, a equals 4 and b equals 36.

    Hint: you can always estimate values for a and then you solve, and whatever you get as your answer will be b.

  • Caculus f'(x) -

    y = ax^3
    y' = 3ax^2
    at x=-2, y' = 12a
    The line y=2x+b has slope 2, so
    12a=2
    a = 1/6

    at x = -2, y = -8a = -4/3 so the line must go through (-2,-4/3)

    So, the tangent line has slope 2 and goes through (-2,-4/3)

    y = 2x+b
    -4/3 = -4 + b
    b = 8/3

    So, now we have

    y = 2x - 8/3
    is tangent to
    y = 1/6 x^3
    at (-2,-4/3)

    To confirm this, visit

    http://www.wolframalpha.com/input/?i=plot+y+%3D+1%2F6+x^3+and+y+%3D+2x%2B8%2F3+for+x+%3D+-4+..+4

  • Caculus f'(x) - typo -

    typo near the end

    y = 2x + 8/3

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