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anonymous

  • one year ago

Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of f(3) − f(1)? ?≤ f(3) − f(1) ≤? Im not really sure how to do this, the examples that i have aren't like this one, please help!

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  1. anonymous
    • one year ago
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    4 ≤ f '(x) ≤ 5 means the slope of the tangent line is between 4 and 5. The slope of the secant line from 1 to 3 is \[m = \frac{ f(3)-f(1) }{ 3-1 }=\frac{ f(3)-f(1) }{ 2 }\] So I think to get your answers you need to solve \[4 ≤\frac{ f(3)-f(1) }{ 2 }≤5\]

  2. anonymous
    • one year ago
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    what would i plug in for f(3) though?

  3. freckles
    • one year ago
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    From your question it looks like you want to solve for f(3)-f(1)

  4. freckles
    • one year ago
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    do you know how to undo division an equation... hint multiply by something that un does it

  5. freckles
    • one year ago
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    and this an inequality not an equation but basically works the same way

  6. anonymous
    • one year ago
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    okay so i get 8<f(3)-f(1)<10

  7. anonymous
    • one year ago
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    got it thanks!!

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