Purchase Solution

Word Problem : Intermediate Value Theorem

Not what you're looking for?

Ask Custom Question

At 8am on Saturday, a man begins running up the side of a mountain to his weekend campsite. On Sunday at 8am, he runs back down the mountain. It takes him 20 minutes to run up, but only 10 minutes to run down. At some point on his way down, he realizes that he passed the same exact place at exactly the same time on Saturday. Prove that he is correct.(hint:Let u(t) and d(t) be the position functions for the runs up and down, and apply the intermediate value theorem to f(t)=u(t)-d(t).

Purchase this Solution
Solution Summary

The Intermediate Value Theorem is applied to solving a relative time and distance problem.

Solution Preview

Ok, we consider f(t)=u(t)-d(t) where u(t) shows the position function for run up and d(t) shows the position function for run down. We should define a direction and stick to it till the end. Let's say the start point is the origion ...

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Domain, Continuity and the Intermediate Value Theorem

    117847 Domain, Continuity and the Intermediate Value Theorem 56.

  • Intermediate value theorem

    202678 Intermediate value theorem problem See attached for circled problems Suppose that a function f is continuous on [0,1] except at 0.25 and that f(0)=1 and f(1)=3.....

  • Intermediate value theorem

    Intermediate value theorem: If is continuous on a closed interval and there exists a number c such that then there is at least one number such that Mean Value Theorem.

  • Monotonic functions

    475628 Monotonic functions Give an example to show that the intermediate value theorem becomes false if the hypothesis that f is continuous is replaced with f being montone, or with f being strictly monotone.

  • Root of the Problem Descriptions

    This is how I tried to solve it: I used the interval [-1,1] By the Intermediate Value Theorem, since f(0) is between (-1,1), f(0) is the only root. --- Please see the attachment. First, I solve this problem. , .

  • Intermediate value theorem

    16641 Intermediate value theorem Define Intermediate-Value theorem Using this theorem, show that there is a root of P(x)=x^3+x^2+x-1 in the closed interval [0,1]. P(x) is continuous.

  • Intermediate Value Theorem : Zero Value

    557591 Intermediate Value Theorem : Zero Value 1. Using the intermediate Value theorem, show that the function f has a zero between a and b. f(x)=x^3+3x^2-9x-13, a=-5, b=-4 2.

  • Intermediate value theorem

    49605 Intermediate value theorem Determine if the following conforms to the intermediate value theorem. Clearly give the conditions and, if appropriate, find an appropriate value for c.

  • Proof using the Intermediate value theorem

    475627 Proof using intermediate value theorem Let f : [0,1]-->[0,1] be a continuous function. Show that there exists a real number x in [0,1] such that f(x)=x (apply the intermediate value theorem to the function f(x) -x).

View More Related Solutions