Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 523

Average Rate of Change

1. Show that a constant f(x) = b has an average rate of change of zero.

2. Compute the average rate of change of y = sqrt{4 - x^2} on the interval [-2, 2]. Explain how this can occur.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,184

Re: Average Rate of Change

This is another secant question.

Rate of change means how y is varying with x so it's a gradient that is needed.

For the first part do the usual x and x+h thing.  You should find that the secant function simplfies to zero.

For the second part work out y1 when x = -2 and y2 when x = +2

Then get the gradient of the line joining these two points.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 523

Re: Average Rate of Change

This is another secant question.

Rate of change means how y is varying with x so it's a gradient that is needed.

For the first part do the usual x and x+h thing.  You should find that the secant function simplfies to zero.

For the second part work out y1 when x = -2 and y2 when x = +2

Then get the gradient of the line joining these two points.

Bob

In place of using the difference quotient, can I take the derivative the y = sqrt{4 - x^2} as step one?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,184

Re: Average Rate of Change

Because 1 says 'show' just saying what the derivative is would not be enough.

For 2, differentiation wouldn't work because an average is asked for.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 523

Re: Average Rate of Change

Because 1 says 'show' just saying what the derivative is would not be enough.

For 2, differentiation wouldn't work because an average is asked for.

Bob

Ok. I will use the difference quotient to follow through with this problem.