5. Let f be continuous on (a, b) and differentiable on (a, b). Assume that m< f'(x) < M for all a e (a, b). Show that m+ M am + bM f(b) + f(a) m+ M bm + aM for all z € (a, b).
5. Let f be continuous on (a, b) and differentiable on (a, b). Assume that m< f'(x) < M for all a e (a, b). Show that m+ M am + bM f(b) + f(a) m+ M bm + aM for all z € (a, b).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:5. Let f be continuous on (a, b) and differentiable on (a, b). Assume that m < f'(x) < M for all a e (a, b).
Show that
m + M
am + bM
S(b) + S(a)
m+ M
bm +aM
S S(x) –
2
2
for all a € (a, b).
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