Question

Find the average rate of change of the function y = x^2 - 3x + 5 over the interval [-1,3]

Answer 1

\[\frac{f(3)-f(-1)}{3--1}\]

Answer 2

hopefully, you know what f(3) and f(-1) mean :)

Answer 3

f(3) = 3^2 - 3(3) + 5 = 5

f(-1) = (-1)^2 -3(-1) + 5 = 10

Answer 4

5 - 10
----- = avg rate of change
4

Answer 5

3+1 = 4 + 5 = 9 , not 10

Answer 6

sooo close lol

Answer 7

5-9
---- = -1 then :)
4

Answer 8

yes, thank you it is the derivative of b minus deriv of a, all over function b - function a

Answer 9

right...

Answer 10

derivatives are instantaneous rates of change; average rates are just last - first divided by well, b-a

Answer 11

i wonder if derivs work out as well

2x-3; 2-3 = -1 , 6-3 = 3

-1-3
---- = -1 hmmm, might be on to something there
3+1

Answer 12

you are just looking for the slope of the secant line that lies on the curve y=x^2-3x+5 touching the two points (-1,f(-1)) and (3,f(3))

Answer 13

nope, 2(-1)-3 = -5

Answer 14

so basically you learn how to find average rate of change in algebra

Answer 15

its just the slope of a line

Answer 16

farm says I shouldnt harass you for your banning techniques :)

Answer 17

shhh i will accidentlly ban you

Answer 18

:) practice makes perfect

Answer 19

wait, i am confused a little bit, what do i do in simple steps to solve this?

Answer 20

(3^2-3(3)+5) - ((-1)^2-3(-1)+5)
-----------------------------
3-(-1)

Answer 21

that is equal to -1 right

Answer 22

the avg rate of change is just the slope of the line between 2 points

Answer 23

the instant rate of change is the slope of the tangent line to the curve at a point; also known as the derivative

Answer 24

okay, i'm good

Answer 25

yay!! :)