Question

average rate of change of a function, f(x)= 9x-15 as x changes from 3 .

Answer 1

The average rate of change of a continuous function, f(x) , on the closed interval [a,b] is given by

f(b)−f(a)b−a

Basically, the average rate of change tells us how, on average, the y-value of a function is changing per unit change in the x-value.

The average rate of change formula is just a variation of the slope formula

y2−y1x2−x1

since y=f(x).

Let's let f(x)=−x2+8x−9.

The average rate of change on the closed interval [2,5] is given by

f(5)−f(2)5−2=6−35−2=33=1

This is also the slope of the secant line to the graph of f through the points (2,3) and (5,6)