## A community for students. Sign up today

Here's the question you clicked on:

## David_Ho 4 years ago Give the number of values of c that verify the mean value theorem for f(x) = sin(x) on the interval [-1,5].

• This Question is Closed
1. naf

|dw:1317571240881:dw|

2. David_Ho

Hiya! So far I have cos(x) = (sin(5) - sin(-1))/4 I really have no clue where to go with that.

3. naf

|dw:1317571301234:dw|

4. elecengineer

Find a value for the RHS

5. elecengineer

then you can figure out how many solns for x are in the interval

6. JamesJ

What is C here? (And btw, the derivative isn't a feature of the MVT.)

7. naf

|dw:1317571400618:dw|

8. naf

|dw:1317571475430:dw|

9. JamesJ

I think I see. Look at f(-1) and f(5). Then the MVP says for every y such that f(-1) < y < f(5) there is a c such that f(c) = y. Is that what you're asking about?

10. elecengineer

c is a value of x

11. David_Ho

Well, what I've recently learned is that MVT is (f(a) - f(b))/b -a = f' (c)

12. David_Ho

I had this problem earlier where I had to find the c value.

13. JamesJ

Ok, that's another MVT, sometimes called Rolle's theorem. But be that as it may, we'll use the one you're talking about. Here a = -1, b = 5. What is the LHS that expression?

14. David_Ho

What is LHS? sorry

15. elecengineer

Rolle's theorm is a specific case of MTV

16. David_Ho

oh ok, it would be the derivative of f(x) or cos(x)

17. JamesJ

the left hand side LHS

18. David_Ho

cos(x) = (sin(5) - sin(-1))/4

19. David_Ho

replace x for c

20. JamesJ

Right. so solutions to this equation are teh values c you're looking for. Remember also that c must lie between -1 and 5 So how many such solutions are there?

21. JamesJ

Actually no -- check your equation carefully . It is NOT divided by 4.

22. naf

|dw:1317572230820:dw|

23. David_Ho

ohh, divide by 6.

24. David_Ho

There would only be one value, right? Since there are only constants on the right side the value of c can only be one value. Is this logic sound?

25. JamesJ

No, it is not sound, because the function cos x isn't 1:1; it has periodicity; it goes up and down with period 2pi, which is almost exactly equal to the length of the interval [-1.5]. So there MIGHT be one c, but there could easily be two values of c. So you are going to have to calculate explicitly and check.

26. David_Ho

oohh, alright. I see what you mean now. I have to find all of the points on cos x that have a tangent line = to (sin(5)-sin(-1))/6.

27. JamesJ

No you need to find x such that cos x = (sin(5)-sin(-1))/6

28. JamesJ

cos x is the formula for the slope of the tangents to sin x. That's what we're looking for.

#### Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy