Answer:
11.
Step-by-step explanation:
We have been given a function [tex]p(x)= x^2+6x+5[/tex] and we are asked to find the the average rate of change from x = 2 to x = 3.
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Average rate of change}=\frac{p(3)-p(2)}{3-2}[/tex]
Let us find p(3) by substituting x=3 is our given formula.
[tex]p(3)=3^2+6*3+5[/tex]
[tex]p(3)=9+18+5[/tex]
[tex]p(3)=32[/tex]
Let us find p(2) by substituting x=2 is our given formula.
[tex]p(2)=2^2+6*2+5[/tex]
[tex]p(2)=4+12+5[/tex]
[tex]p(2)=21[/tex]
Let us substitute values of our function at x = 2 and x = 3 in average rate of change formula.
[tex]\text{Average rate of change}=\frac{32-21}{3-2}[/tex]
[tex]\text{Average rate of change}=\frac{11}{1}[/tex]
[tex]\text{Average rate of change}=11[/tex]
Therefore, the average rate of change for our given function from x=2 to x=3 is 11.
Answer:
= 11
Step-by-step explanation:
The average rate of change of f(x) over an interval between 2 points (a ,f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
Therefore;
= (f(b)- f(a))/(b-a)
a = 2, b= 3
f(2) = 2² + 6(2) +5
f(2) =21
f(3) = 3² + 6(3) + 5
f(3) = 32
Thus; the rate of change will be;
= (32-21)/(3-2)
= 11
This means that the average of all the slopes of lines tangent to the graph of f(x) between (2,21) and (3 ,32) is 11.
