What is the rate of change on the interval [-1,2] ?

Question

I don’t understand how to do this. 

Answer 1

You need a function in addition to the intervals to determine the rate of change.  What is rate of change?  It's just slope.

 

Remember the slope formula: Y₂-Y₁/X₂-X₁

 

Take the function f(x) = X²-X for example.  The interval [-1,2] are just x-values that you have to plug into the function.

 

So, if I plug in -1 for x into the function, I get: f(x)=(-1)²-(-1) = 2.  Then, if I plug in 2 for x into the function, I get: f(x)=(2)²-2 = 2.  

 

Then you list as coordinate pairs or in a table:

 

(-1, 2)

(2, 2)

 

Finally,  you use slope formula to calculate the rate of change:

 

2-2/2-(-1) = 0/3 = 0.  So the rate of change for f(x) =X²-X over the interval [-1,2] is 0.