2009-11-15, 11:42 PM
Mean Value Theorem states that there must exist some value c in [4, 8] for which f'© equals the mean value of f'(x) over [4, 8], i.e. the slope from 4 to 8, rise over run: f(8)-f(4) / 8-4.
So, for any value of c:
-5 ≤ f'© ≤ 3
-5 ≤ f(8)-f(4) / 4 ≤ 3
-20 ≤ f(8)-f(4) ≤ 12
So, for any value of c:
-5 ≤ f'© ≤ 3
-5 ≤ f(8)-f(4) / 4 ≤ 3
-20 ≤ f(8)-f(4) ≤ 12