Asked by Anjoy Aru
verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.
f(x)=√x-1/3 x,[0,9]
f(x)=√x-1/3 x,[0,9]
Answers
Answered by
oobleck
(f(9)-f(0))/9 = (0-0)/9 = 0
Since f(0) = f(9) we can apply Rolle's Theorem.
f'(x) = 1/(2√x) - 1/3
So, look for some value x=c such that f'(c) = 0
1/(2√c) = 1/3
2√c = 3
c = 9/4
Since f(0) = f(9) we can apply Rolle's Theorem.
f'(x) = 1/(2√x) - 1/3
So, look for some value x=c such that f'(c) = 0
1/(2√c) = 1/3
2√c = 3
c = 9/4
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.