What is the average rate of change between x=0 and x=5 for the equation y=-x²+6x+5?

Question

Please help 

Answer 1

Let      f(x) = -x² + 6x + 5

 

 

Average rate of change is then

 

 

f(5) - f(0)

_________

   5 - 0

 

 

 

Another way you can get the average rate of change is to plot the points of a graph from x=0 to x=5.

 

Point 1 = (0, f(0))

Point 2 = (1, f(1))

Point 3 = (2, f(2))

Point 4 = (3, f(3))

Point 5 = (4, f(4))

Point 6 = (5, f(5))

 

 

You will connect the 6 points together in the order plotted, but in straight lines rather than a curve.  You should have 5 straight lines once you connected them.  Find the slope of each line.  Then take the average of the slopes.