Can u please answer question 4 Could you please show your st

3. Given the function g(x) 8x% defined on t1,11, determine if the function satisfies the Mean Value Theorem. If so, find the value \"c\" guaranteed by the Mean Value Theorem and interpret its meaning. If not, explain why not. 4. Two stationary patrol cars equipped with radar are 6 miles apart on a highway. A truck passes a patrol car and its speed is clocked at 55 mph. 5 minutes later when the truck passes the second patrol its speed is clocked at 50 mph. Use the Mean Value Theorem to prove that the truck driver must have exceeded the speed limit of SS mph sometimes during the 5 minutes.

Solution

Time taken = 5/60 = 1/12 hours

Now, s(t) represents the distance travelled by the truck from the first patrol car to the second patrol car

s(0) = 0, s(1/12) = 6

average velocity = s(1/12) - s(0)/(1/12 - 0)

=> (6 mi - 0)/(1/12)

=> 72 miles/hour

Hence applying the mean value theorem we can say that the truck was travelling at a speed of 72 miles/hour in his five minute journey