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Math Help - Limits

  1. #1
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    Limits

    Suppose that a function f is differentiable at x = 1 and
     \\lim_{h \to 0} \frac{f(1 + h)}{h} = 5

    Find f(1) and f '(1).


    So, dy/dx at x = 1 is 5.

    So the equation of the tangent line is y - f(1) = 5(x - 1).

    But how can I find f(1)?
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  2. #2
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    Re: Limits

    Is my approach right?

    I think if it is differentiable at x = 1, then it is also continuous at x = 1.

    Then...

    Any idea would be appreciable.
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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Limits

    This is what I think:
    In general the definition of the derivative is:
    lim_(h->0) (f(x+h)-f(x))/h = df(x)/dx
    You have given a function which is differentiable at x=1 so:
    lim_(h->0) (f(1+h)-f(1))/h = f'(1)
    If you compare this with the given limit: f(1) = ...
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