Question: Theorem 1. If f is a continuous function on the closed interval [a, b] and differ- entiable on the open interval (a, b), then

Theorem 1. If f is a continuous function on the closed interval [a, b] and differ- entiable on the open interval (a, b), then there exists a point c in the interval (a, b) such that f'(c) f(b)-f(a) = b-a Try to use it to solve the next problem. Problem 2. A car traverses a tunel which is 1km long in 50 seconds. If the speed limit inside the tunel is 60 km/h, can we guarantee that the car went over the speed limit?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

In analyzing hits by certain bombs in a war, an area was partitioned into 574 regions, each with an area of 0.95 km. A total of 525 bombs hit the combined area of 574 regions. Assume that we wan to...

Please provide with explanations 99'? Suppose f(x) =(1+] . Investigate lim f(x) using the table provided and Your graphing x xFCD calculator. Follow the steps provided below. [Refer to Textbook page...

Use the Intermediate Value Theorem from Section 2.5 to show that (x) = x 3 + 2x - 4 has a root between x = 1 and x = 2. Then find the root to five decimal places. Intermediate Value Theorem from...

I would like get help with this question and be sure to show steps please be clear with your solution. Thank you for the help Suppose that f is a continuous function on the closed interval [a, b ....

6. The Mean Value Theorem for Integrals states that a continuous function on a closed interval takes on its average value at the same point in that interval. The theorem ensures that if f (@ ) is...

EVT Practice (4 questions/Please show work) 4. [2009 BCZ, part b only] The rate at which people enter an auditorium for a rock concert is modeled by the function R given by R(t) = 1380:2 675:3 for 0...

Consider the Mean Value Theorem: If f is a continuous function on the closed interval [a,b], and differentiable on the open interval (a,b), then there exists at least one point c (a,b) such that ....

6 Calculus questions pls help If f {m} = :.:2 + m, which of the following would give the derivative of the function? (ch+x+.i_l.;t:)(:t:2 +x) Ax _ 2 _ _ 2 (B) \"max>0[ (x+x) +(:+:x)] ( :1: +x) (C) [...

7-According to the Mean Value Theorem for Integrals if f is a continuous function on the closed interval [a,b], then there exists a number c between a and b such that (10 pts.) b I f (10:11: = (b...

hi there, can someone please provide a full detailed solution to the following Calc 1 questions. thank you Suppose f is a continuous function on the closed interval [4, 8] and the following values of...

Using Table H, find the P-value interval for each F test value. a. F = 2.97, d.f.N. = 9, d.f.D. = 14, right-tailed b. F = 3.32, d.f.N. = 6, d.f.D . =12, two-tailed c. F = 2.28, d.f.N. = 12, d.f.D. =...

. A fund investing in a mix of stocks and bonds is probably a A ) Money market fund B ) Balanced fund C ) Sector fund D ) Growth fund

A hula hoop and solid disc of equal radii are rolled, from rest and without slipping, down an incline plane. Which one will reach the bottom of the inclined plane first? Explain.

How does management determine how to classify each type of output from a joint process? Is this decided before or after production? LO1.

Why is cost allocation necessary in accounting? Why is it necessary in a joint process? LO1.

By what criteria would management determine whether to proceed with processing at each decision point in a joint production process? LO1.