Suppose that f(0)=3 and f′(x)≤7 for all values of x. use the mean value theorem to determine how large f(4) can possibly be.

With these given values:

 f(0)=4 and f′(x)≤4 

The solution is as follows:

 f(0) = 4 
f ' (x) ≤ 4 for all x 

The Mean Value Theorem says there is a c between 0 and 4 such that f ' (c) = [f(4) - f(0)] / (4 - 0) 
But since f ' (x) ≤ 4 for all x, then [f(4) - f(0)] / (4 - 0) ≤ 4 
Since f(0) = 4, then [f(4) - 4] / (4 - 0) ≤ 4 
Multiplying both sides by 4 you get f(4) - 4 ≤ 16 
Adding 4 to both sides you get f(4) ≤ 20 

So f(4) ≤ 20

By examining the solution, it could guide you on answering the problem on your own. Hope that helps

13 hours should be your answer. divide 576 by 8. divide 936 by your answer