# Thread: Mean Value Theorem- Need help tonight please

1. ## Mean Value Theorem- Need help tonight please

Hey everyone, just reached a problem in my homework that I'm not sure how to do... hopefully someone will be of some help.

Clark is driving by car 213 miles from Fort Worth to Austin. He took exactly 3 hours on his trip and made no stops. Using the Mean Value Theorem, prove that at some point Clark went above 70 mph. At what time was Clark speeding?

Thanks for your help.

2. Originally Posted by jynxed27
Hey everyone, just reached a problem in my homework that I'm not sure how to do... hopefully someone will be of some help.

Clark is driving by car 213 miles from Fort Worth to Austin. He took exactly 3 hours on his trip and made no stops. Using the Mean Value Theorem, prove that at some point Clark went above 70 mph. At what time was Clark speeding?

Thanks for your help.
The average velocity over the three hours is given by 213 miles/3 hours = 71 mph. The Mean Value Theorem then implies that at some point, he was going exactly 71 mph.

3. Using M.V.T. you have starting position 0 miles and final destination 213 miles. Using M.V.T you have:

(231-0 miles)/(3 hours) = 71 mph. So at some point the car ecxeeded 70 mph.

However I'm not sure how to find the time since you weren't given any function.