Assume that abs[f '(x)] ≤ M for a ≤ x ≤ b. One can show by the Mean Value Theorem that abs[f(b) − f(a)] ≤ M (b − a), and thus f(a) − M(b − a) ≤ f(b) ≤ f(a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17 (Hint: Let f (x) = x, a = 100, and b = 101, and then find bounds for f(101) = sqrt(101).
First, find a reasonable value for M: M = ______

Question

Assume that abs[f '(x)] ≤ M for a ≤ x ≤ b. One can show by the Mean Value Theorem that abs[f(b) − f(a)] ≤ M (b − a), and thus f(a) − M(b − a) ≤ f(b) ≤ f(a) + M(b − a). Using this fact, determine a lower bound and an upper bound for 17 (Hint: Let f (x) = x, a = 100, and b = 101, and then find bounds for f(101) = sqrt(101). 
First, find a reasonable value for M: M = ______