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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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!

Mathematics
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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 \[4 ≤\frac{ f(3)-f(1) }{ 2 }≤5\]
what would i plug in for f(3) though?
From your question it looks like you want to solve for f(3)-f(1)

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Other answers:

do you know how to undo division an equation... hint multiply by something that un does it
and this an inequality not an equation but basically works the same way
okay so i get 8
got it thanks!!

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