Answer:
The rate of change for the given function between x=3 and x=7 is 19
Step-by-step explanation:
Given function is:
[tex]y = x^2+9x[/tex]
Can also be written as:
[tex]f(x) = x^2+9x[/tex]
The rate of change of a function is given by the formula:
[tex]Rate\ of\ change = \frac{f(b)-f(a)}{b-a}[/tex]
In the given question,
We have to find rate of change between 3 and 7
Here
b = 7 and a = 3
WE have to find f(7) and f(3) first
So,
[tex]f(7) = (7)^2+9(7) = 49 + 63 = 112\\f(3) = (3)^2 + 9(3) = 9+27 = 36[/tex]
Putting the values in the formula
[tex]Rate\ of\ change = \frac{112-36}{7-3}\\=\frac{76}{4}\\=19[/tex]
Hence,
The rate of change for the given function between x=3 and x=7 is 19
