Question

Find the average rate of change of the function from x = 1 to x = 2. f(x) = − 2 /x^2

Answer 1

`(7)/(4)}\\\\`

Explanation:

Find the average rate of change of

`f\left(x\right)=- (2)/(x^(3))`
over the interval [1, 2]

`\textrm{ The average rate of change of $f(x)$ on the interval [a,b] is $(f(b)-f(a))/(b-a)$}`

`\textrm{We have that a = 1, b = 2 }`
`f\left(x\right)=- (2)/(x^(3))`

`f(2) = -(2)/(2^3) = --(2)/(8) = -(1)/(4)\\\\`

`f(1) = -(2)/(1^3) = -2`

`f(2) - f(1) = -(1)/(4) - (-2) = -(1)/(4) + 2\\\\= 2 -(1)/(4) = (8)/(4) - (1)/(4) = (7)/(4)`

b- a = 2 -1 =1

`\text{So average rate of change = $(7)/(4) / 1$} = (7)/(4)}\\\\`