Question

Given the function :f(x) = 3x^2 - 4x + 1Find the average rate of change of f on [-3, 2]:

Answer 1

Given function is,

`f\mleft(x\mright)=3x^2-4x+1`

To find the average rate of change of f on [-3, 2]

we know that, average rate of change of a function a on the two points x=a and x=b is,

`=(f(b)-f(a))/(b-a)`

Using this we get,

Average rate of change is,

`=(f(2)-f(-3))/(2-(-3))`
`=(3(2)^2-4(2)+1-(3(-3)^2-4(-3)+1))/(5)`
`=(3(4)-8+1-3(9)-12-1)/(5)`
`=(-35)/(5)`
`=-7`

Average rate of change is -7

Answer is: -7