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Math Help - Linear approximation help.

  1. #1
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    Linear approximation help.

    Part b. I need help with. I don't get it! Please help!
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  2. #2
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    Re: Linear approximation help.

    the tangent line, y = -3x+7 , serves as an approximation of function values close to x = 2.

    f(x) \approx -3x+7 for values of x close to x = 2.

    f(2.1) \approx -3(2.1)+7

    f(1.98) \approx -3(1.98)+7

    ... as far as an "over" or "under" estimate, look at the tangent line and the concavity of f(x) on both sides of x = 2.

    ... the tangent line and f(x) have the same value at x = 2. What do you think happens to the accuracy of the approximation as x gets farther away from x = 2?
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  3. #3
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    Re: Linear approximation help.

    Book has f(2.1),overestimate and f(1.98), underestimate. That part I don't get, should it be the other way? I get that the second approximation, f(1.98), is better because it is closer to 2. The over and under is throwing me off! Thanks for your reply.
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  4. #4
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    Re: Linear approximation help.

    "book" has it backwards w/r to over and underestimates
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