Question

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

Answer 1

I think this is a fundamental theorem of calculus question:
http://www.sosmath.com/calculus/integ/integ03/integ03.html
http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html

Answer 2

I'll come back to this later tonight when i have more time.

Answer 3

From 3 ≤ f '(x) ≤ 5,

for maximum value, f'(x) = 5\[\Large \int\limits_{3}^{5} 5 dx = F(5) - F(3)\]
for min value, f'(x) = 3
\[\Large \int\limits\limits_{3}^{5} 3 dx = F(5) - F(3)\]

Answer 4

So to find the maximum you just need to integrate \[\Large \int\limits\limits_{3}^{5} 5 dx =\]
And to find the minimum you integrate \[\Large \int\limits\limits_{3}^{5} 3 dx =\]