# Word Problems : Derivatives and Rate of Change

Not what you're looking for?

41) Suppose that the average yearly cost per item for producing x items of a business product is C(x)=10+(100/x) . if the current production is x=10 and production is increasing at a rate of 2 items per year, find the rate of change of the average cost.

45) Suppose a 6ft tall person is 12 ft away from a 18-ft tall lamppost. if the person is moving away from the lamppost at a rate of 2 ft/s, at what rate is the length of the shadow changing? (Hint: show that (x+s)/18=s/6.)

47) Suppose that a raindrop evaporates in such a way that it maintains a spherical shape. given that the volume of a sphere of radius r is V=(4/3)(phi)r², if the radius changes in time, show that V'=Ar'. If the rate of evaporation (V') is proportional to the surface area, show that the radius changes at a constant rate.

##### Purchase this Solution

##### Solution Summary

Three rate of change problems are solved. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Solving quadratic inequalities

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

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Probability Quiz

Some questions on probability