Question

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!

Answer 1

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
\[4 ≤\frac{ f(3)-f(1) }{ 2 }≤5\]

Answer 2

what would i plug in for f(3) though?

Answer 3

From your question it looks like you want to solve for f(3)-f(1)

Answer 4

do you know how to undo division an equation...
hint multiply by something that un does it

Answer 5

and this an inequality not an equation but basically works the same way

Answer 6

okay so i get 8<f(3)-f(1)<10

Answer 7

got it thanks!!