# Math - Instantaneous and average rates of change

a) Describe a graph for which the average rate of change is equal to instantaneous rate of change for its entire domain. Describe a real life situation that this graph could represent.

b) Describe a graph which the average rate of change between two points is equal to the instantaneous rate of change at:
i) one of the two points
ii) the midpoint between two points

c) Describe a real life situation that could be represented by each of the graphs in part b)

1. 👍
2. 👎
3. 👁
1. a)
The equivalent statement is that:
since the instantaneous rate of change is equal to the average rate of change throughout the domain, the instantaneous rate of change does not vary.

How would you describe a function for which the instantaneous rate of change does not vary?

b)
The mid-point theorem in mathematics says that the average rate of change of a function between two points is equal to the instantaneous rate of change of at least one point between the two end-points. Therefore the graph of any curve would satisfy condition (b)(i).
For part b)(ii), you need to draw a graph in which the tangent to the curve at the mid-point is equal the chord joining the two end-points.

1. 👍
2. 👎

## Similar Questions

1. ### Math (calculus) (mean values)

A company introduces a new product for which the number of units sold S is given by the equation below, where t is the time in months. s(t)=155(7-9/(2+t)) a) Find the average rate of change of s(t) during the first year. Which my

2. ### math

An investment of 25,000 earns interest at an annual rate of 8.4% compounded continuosly a. find the instantaneous rate of change of the amount in the account after years b. find the instantaneous rate of change of the amount in

3. ### math

Determine which function has the greater rate of change in questions 1−3 1. x y ------- -1 0 0 1 1 2 2 3 (1 point) The rates of change are equal. The graph has a greater rate of change.*** The table has a greater rate of change.

4. ### calculus

No idea where to start The cost in dollars of producing x units of a particular camera is C(x) = x2 - 10000. (10 points) Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x

1. ### Physics

When is the average velocity of an object equal to the instantaneous velocity? a) always b)never c) only when velocity is constant d)only when velocity is increasing at a constant rate c) would be the answer since you could cross

2. ### Math

A batter hits a baseball straight up into the air. The height of the ball in metres above the ground is given by h(t)=-4.9t^2+23t+2, where t is the number of seconds after the ball is hit. a) What is the average rate of change in

3. ### mathematics

The Cost (in dollars) of producing x units of a certain commodity is C(x) = 500 + 10x + 0.005x 2 i. Find the average rate of change of C with respect x when the production level is from x = 100 to x = 105 units.  ii. Find the

4. ### calculus (rate of change)

consider the function f(x)=x^2-6x+12 a. find the average rate of change over the interval [-1,3] b. use the definition of the derivative to find f prime(x) c. find the instantaneous rate of change at the point where x=3 d. find

1. ### Mathematics

Examine the following graph of the linear function f(x)=2x+1 and the quadratic function g(x)=−116(x+3)2+6. Graph of g of x is a downward opening parabola that passes through points (negative 4, 5), (negative 3, 6), & (1, 5). f

2. ### precalculus

Can someone verify if my answer is right? 1. Which function has a negative average rate of change on the interval 1

3. ### Calc

The wind chill is the temperature, in degrees Fahrenheit, a human feels based on the air temperature, in degrees Fahrenheit, and the wind velocity (v), in miles per hour (mph). If the air temperature is 32degrees Fahrenheit, then

4. ### Calculus

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis