Posted by Ashley on .
use mean value theorem:
f(x)= 7 2^x, [0,4], c=?

Calculus 
Steve,
f(4) = 9
f(0) = 6
so, we want f'(c) = 15/4
f'(x) = ln2 2^x
15/4 = ln2 2^c
15/(4ln2) = 2^c
ln(15/ln16) = c ln2
c = ln(15/(4ln2))/ln2 = 2.4356
which is in the interval [0,4]