f(x)= (x-3)^2
find the average rate of change between the following points:
a) x=1 and x=3
b) x=4 and x=7
recall that the average rate of change on [a,b] is
(f(b)-f(a))/(b-a)
now just plug and chug.
is it 1?
Nope. Show your work, and we can see what went wrong.
Don't forget your Algebra I now that you're taking calculus...
a) 4&0
b) 1&16
not sure if im suppose to subtract these giving me a=4 and b=15
after my calculations i got that a=2 and b=5???
i meant -2
To find the average rate of change of a function between two points, we will use the formula:
Average Rate of Change = (f(x₂) - f(x₁)) / (x₂ - x₁)
a) For points x = 1 and x = 3:
Step 1: Substitute the values of x into the function f(x) = (x - 3)^2
f(1) = (1 - 3)^2
= (-2)^2
= 4
f(3) = (3 - 3)^2
= 0^2
= 0
Step 2: Calculate the average rate of change using the formula:
Average Rate of Change = (f(3) - f(1)) / (3 - 1)
= (0 - 4) / (3 - 1)
= -4 / 2
= -2
Therefore, the average rate of change between x = 1 and x = 3 is -2.
b) For points x = 4 and x = 7:
Step 1: Substitute the values of x into the function f(x) = (x - 3)^2
f(4) = (4 - 3)^2
= 1^2
= 1
f(7) = (7 - 3)^2
= 4^2
= 16
Step 2: Calculate the average rate of change using the formula:
Average Rate of Change = (f(7) - f(4)) / (7 - 4)
= (16 - 1) / (7 - 4)
= 15 / 3
= 5
Therefore, the average rate of change between x = 4 and x = 7 is 5.