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Math Help - Derivatives

  1. #1
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    Derivatives

    Suppose f has the values shown below:

    f(1.9)=6.6, f(1.97)=6.905, f(2.0)=7, f(2.02)=7.059, f(2.2)= 7.5

    Use the tabulated values of f to estimate.

    1) f'(1.9)
    The book says the answer to #1 is f'(1.9)= 4.357
    2)f'(1.97)

    Use the values f(1.9), f(1.95), f(2.0) and f(2.01) to estimate
    (a) f'(1.9)
    (b)f'(2.0)
    (c)f'(2.01)

    3) f(x)=x^2
    the book says the answer for this one is
    (a) -3.85
    (b) 4.01
    (c) 4.01

    For both questions I do no understand how to get these answers. Am I suppose to use a formula? I would I go about solving these I do not understand derivatives well. Please explain I need to understand. Thank you.
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  2. #2
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    Quote Originally Posted by asweet1 View Post
    Suppose f has the values shown below:

    f(1.9)=6.6, f(1.97)=6.905, f(2.0)=7, f(2.02)=7.059, f(2.2)= 7.5

    Use the tabulated values of f to estimate.

    1) f'(1.9)
    The book says the answer to #1 is f'(1.9)= 4.357
    2)f'(1.97)

    Use the values f(1.9), f(1.95), f(2.0) and f(2.01) to estimate
    (a) f'(1.9)
    (b)f'(2.0)
    (c)f'(2.01)

    3) f(x)=x^2
    the book says the answer for this one is
    (a) -3.85
    (b) 4.01
    (c) 4.01

    For both questions I do no understand how to get these answers. Am I suppose to use a formula? I would I go about solving these I do not understand derivatives well. Please explain I need to understand. Thank you.
    You are asked to use the slope of the secant (= the slope of the straight line between 2 points) as an approximate value of the slope of the tangent (=f'(x)):

    You know 2 points: P(1.9, 6.6), Q(1.97, 6.905)

    then the slope of the line PQ is:

    m_{PQ}=\dfrac{6.905 - 6.6}{1.97 - 1.9}=\dfrac{0.305}{0.07} \approx 4.32857...

    The other questions have to be solved in quite the same way.
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  3. #3
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    I still do not understand the second part please help
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