Question

How to find the average rate of change from
f(x)=-x^2+4x+1 from x=3 to x=6?

Answer 1

are you able to compute the value of `f(3)` ?

Answer 2

if not, then replace every x with 3


f(x)=-x^2+4x+1

f(3)=-(3)^2+4(3)+1 ... replace every x with 3

f(3) = _______ (fill in the blank and tell me what you get)

Answer 3

it would equal 4

Answer 4

correct, how about `f(6)` ?

Answer 5

-11

Answer 6

good

Answer 7

now to find the average rate of change, we use this formula

\[\Large V = \frac{f(a)-f(b)}{a-b}\]

V = average rate of change from x = a to x = b. I didn't want to use A because 'a' is already taken

Answer 8

so,

\[\Large V = \frac{f(a)-f(b)}{a-b}\]

\[\Large V = \frac{f(3)-f(6)}{3-6}\]

\[\Large V = \frac{4 - (-11)}{3-6}\]

I'll let you finish up

Answer 9

so v=-5, right?

Answer 10

correct, the average rate of change from x = 3 to x = 6 is `-5`

in a visual sense, this means that the slope of the line through the two points A and B on f(x) is going to be -5

A is the point corresponding to x = 3
B is the point corresponding to x = 6