SOLUTION: Help with a rate of change problem Find the average rate of change of {{{g(x)=x^2-5x+1}}} from x=3 to x=7. Simplify your answer as much as possible.

Algebra ->  Linear-equations -> SOLUTION: Help with a rate of change problem Find the average rate of change of {{{g(x)=x^2-5x+1}}} from x=3 to x=7. Simplify your answer as much as possible.      Log On


   

Question 1181838: Help with a rate of change problem
Find the average rate of change of g%28x%29=x%5E2-5x%2B1 from x=3 to x=7.


Simplify your answer as much as possible.
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Plug in x = 3 to find that
g(x) = x^2-5x+1
g(3) = (3)^2-5(3)+1
g(3) = -5

Repeat for x = 7 to find that
g(7) = 15

Then we can say...
m = rate of change from a to b
m = (g(b)-g(a))/(b-a)
m = (g(7)-g(3))/(7-3)
m = (15-(-5))/(7-3)
m = (15+5)/(7-3)
m = 20/4
m = 5

As you can probably guess, I basically used the slope formula. The rate of change from x = 3 to x = 7 is the same as the slope of the line through (3,-5) and (7,15)

Answer: 5

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The average rate of change is the slope of the line through (3,g(3)) and (7,g(7)).

g(3)=-5; the point on the graph is (3,-5)
g(7)=15; the point on the graph is (7,15)

The slope is (15-(-5))/(7-3) = 20/4 = 5