12:12 PM OOO AT&T; o 30% D oncourse.iu.edu 4b: Problem 4 Prev Up Next (1 pt Supp

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12:12 PM OOO AT&T; o 30% D oncourse.iu.edu 4b: Problem 4 Prev Up Next (1 pt Suppose f is a differentiable function on the open interval (2, 19) and continuous on 12, 19]. If 5 S f (z) S 9 for all 2 S z S 19, with the help of the Mean Value Theorem, how small can f(19) f(2) possibly be? How large can 19 20 possibly be? Note: You can earn partial credit on this problem. Preview Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining. Email instructor

Explanation / Answer

mean value theorem says that for a continuous and differentiable function f(x) in an interval (a,b) , for a number c in this interval

f '(c) = (f(b) -f(a))/(b-a)

for our probelm f '(x) = (f(19) -f(2))/(19-2)    for all x belonging to (2,19)

but given that 5<= f'(x) <= 9

=> 5<=(f(19) -f(2))/17 <=9

=> 85 <= (f(19) -f(2)) <=153

so maximum value of f(19) -f(2) will be 153

and minimum value of f(19) -f(2) will be 85

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