Question

Suppose that 2 ≤ f '(x) ≤ 5 for all values of x. What are the minimum and maximum possible values of
f(6) − f(3)?

Answer 1

I have no idea how to approach this, any type of help welcome :)

Answer 2

Well, if the maximum possible slope is 5, then
\[f(x+3) = 5*3 + f(x)\]
right? Just rise over run stuff... so the maximum would be 15. Likewise, the minimum would be 6.

Answer 3

ahhh okay thank you so much! that makes a lot more sense now haha