Find the average rate of change of the function from X=3 to X=6 using formula F(x) = 6-x^2

Question

Find the average rate of change of the function from X=3 to X=6

 

Using the formula F(x)=6-x^2

 

The average rate of change =  ?

 

please find the exact number, no tolerance..

 

Thank You :-)..... 

Answer 1

Hi Winston.

 

The average rate of change of a function f(x) between a and b is given by:

 

(f(b) - f(a)) / (b - a)

 

Here, your f(x) is 6 - x^2

 

a = 3

b = 6

 

f(b) = 6 - 6^2 = -30

f(a) = 6 - 3^2 = -3

 

So

 

(f(b) - f(a)) / (b - a)

 

= (-30 - -3) / (6 - 3)

 

= -27 / 3

 

= -9

 

Your average rate of change is -9.