mean value theorem

[Dorian Gray]

Greetings once again Mathphiles,


I am having an issue with this problem.


Verify the function satisfies the hyptoheses of the Mean Value theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.


f(x)=x^2-4x+5

In general, I am comfortable with these problems. I do not know why my answer does not match up with my key. I know that it is A. Continuous on the closed interval of [1,5] and differentiable on the open interval (1,5), and I know that I need to do the (f(b)-f(a))/(b-a) and then set my derivative equal to my answer from that, which is what I did in my work. Please let me know if you spot a mistake.

Thank you very much!

 

[srmichael]

Greetings once again Mathphiles,


I am having an issue with this problem.


Verify the function satisfies the hyptoheses of the Mean Value theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.


f(x)=x^2-4x+5

In general, I am comfortable with these problems. I do not know why my answer does not match up with my key. I know that it is A. Continuous on the closed interval of [1,5] and differentiable on the open interval (1,5), and I know that I need to do the (f(b)-f(a))/(b-a) and then set my derivative equal to my answer from that, which is what I did in my work. Please let me know if you spot a mistake.

Thank you very much!


View attachment 1853

From all that I can tell, your work looks correct. Maybe someone else can spot the problem. Probably book error, though.

 

[Dorian Gray]

thank you SrMichael

Thank you SrMichael. It is funny that you say that because the very next problem's answer is (3/2) as well, which I found to be ironic.