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Math Help - Finding the derivative using the tangent line

  1. #1
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    Finding the derivative using the tangent line

    If the line tangent to the graph of function f at the point (1,7) passes through the point (-2,-2), then f '(1) is: A)-5 B)1 C)3 D)7 E)undefined

    I know that the slope of the tangent line is 3 using (y-y)/(x-x)
    Also, I'm thinking that I have to use the mean value theorem but i'm not sure how to apply it to this problem
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  2. #2
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    Quote Originally Posted by rawkstar View Post
    If the line tangent to the graph of function f at the point (1,7) passes through the point (-2,-2), then f '(1) is: A)-5 B)1 C)3 D)7 E)undefined

    I know that the slope of the tangent line is 3 using (y-y)/(x-x)
    Also, I'm thinking that I have to use the mean value theorem but i'm not sure how to apply it to this problem

    The slope of the tangent line to the graph of a derivable function f(x) on a point (x_1,f(x_1)) on the graph is given by f'(x_1).
    You don't need mean value theorems or stuff: the answer is right in front of you.

    Tonio
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  3. #3
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    i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f
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  4. #4
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    Quote Originally Posted by rawkstar View Post
    i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f
    The "derivative of 1" is always zero (0).

    "y-y" also equals zero (0).

    "x-x" also equals zero (0).

    Why are you trying to do calculus if you don't remember how to calculate a slope? You have two points, simply calculate the slope and be done with it.

    These are equivalent concepts:

    1) Slope of the Tangent to the curve at x = c
    2) Value of the derivative of the function evaluated at x = c.

    Point-Slope Form

    (y-y_{1}) = f'(x_{1}) \cdot (x-x_{1})
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  5. #5
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    Quote Originally Posted by rawkstar View Post
    i'm not looking for the derivative of 1 of the tangent line, i need to find the derivative of 1 on the function f

    Read again my answer, or better: read again your book's definitions. You clearly don't understand the definition of tangent line to a (graph of a) function on some point of its graph.

    Tonio
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