The average rate of change is 11
Explanation:
The given function is [tex]f(x)=x^{2}+3 x-2[/tex]
We need to determine the average rate of change for the function from 2 to 6
The average rate of change can be determined using the formula,
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
where [tex]a=2[/tex] and [tex]b=6[/tex]
Now, we shall determine the values of f(2) and f(6) by substituting the values for x = 2 and x = 6 in the function [tex]f(x)=x^{2}+3 x-2[/tex]
Thus, we have,
[tex]f(2)=2^{2}+3 (2)-2[/tex]
[tex]=4+6-2[/tex]
[tex]f(2)=8[/tex]
Similarly, substituting x = 6, we get,
[tex]f(6)=6^{2}+3 (6)-2[/tex]
[tex]=36+18-2[/tex]
[tex]f(6)=52[/tex]
Hence, substituting these values in the formula [tex]\frac{f(b)-f(a)}{b-a}[/tex] , we get,
[tex]\frac{f(b)-f(a)}{b-a}=\frac{52-8}{6-2}[/tex]
Simplifying, we get,
[tex]\frac{f(b)-f(a)}{b-a}=\frac{44}{4}=11[/tex]
Thus, the average rate of change for the function from 2 to 6 is 11
