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Math Help - Tangent lines and area

  1. #1
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    Tangent lines and area

    I need help with this, mainly because it deals with multiple variables.

    f(x) = x^2 + 2

    What is the equation of the line tangent to f(x) at point P(a, f(a)), where 0 < a < 4 ?

    What is the expression for A(x) in terms of a, where A(x) is the area of the triangle formed by the previous tangent line, the x axis, and the line joining P at (4, 0)?

    What is the value of a that makes A(x) a minimum and why?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    1.For your tangent line compute

    y= f ' (a)(x-a) +f(a)

    yes it will contain both x and a

    2. find the x intercept by letting y= 0 and solve for x

    compute the distance from the xintercept to the point (4,0) this is the base of your triangle

    3. A = 1/2 bh the base you have --the height is f(a)

    So A will be a function of a

    4. Maximize the area using the derivative

    It will get messy ---I get a = .745

    If anyone knows of a more clever way I'd like to know.
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  3. #3
    MHF Contributor Calculus26's Avatar
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    that should be .658

    and I used the computer to solve it
    Last edited by Calculus26; April 28th 2009 at 08:19 PM.
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