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[SOLVED] 3.6.26 mvt - Using the mean value theorem to show the change in a function is bounded

karush

Well-known member
Jan 31, 2012
2,678
2020_03_27_11.19.53~2.jpg

Ok Just have trouble getting this without a function..
 
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skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
655
average rate of change of $f(x)$ on the interval $[2,8]$ is $\dfrac{f(8)-f(2)}{8-2}$

the MVT states there exists at least one value of $x \in (2,8)$ where $f'(x) = \dfrac{f(8)-f(2)}{8-2}$

$3 \le f'(x) \le 5 \implies 3 \le \dfrac{f(8)-f(2)}{8-2}\le 5 \implies 18 \le f(8)-f(2) \le 30$