# Mean value theorem problem

1. Sep 19, 2013

### Saitama

1. The problem statement, all variables and given/known data
Suppose that f(0)=-3 and f'(x)<=5 for all values of x. The the largest value of f(2) is
A)7
B)-7
C)13
D)8

2. Relevant equations

3. The attempt at a solution
The problem can be easily solved using the mean value theorem but solving it in a different way doesn't give the right answer and I am not sure if the following is a valid approach.
I have $f'(x) \leq 5 \Rightarrow f(x) \leq 5x+c$, where c is some constant. At x=0, $f(0) \leq c \Rightarrow c\geq -3$.
At x=2, $f(2)\leq 10+c$. The problem is that c can take any value greater than -3 and due to this I reach no answer. What is wrong with this method?

Any help is appreciated. Thanks!

2. Sep 19, 2013

### ehild

f ' (x) = k ≤ 5. Integrating, f=kx+c and f(0)=-3. Therefore C=-3, well determined.

ehild

3. Sep 19, 2013

### Saitama

Really silly on my part, thank you very much ehild! :)