Question

Compute the difference quotient, f(x+h)-f(x)/h , for the function f(x) = 3/2x. Show all algebraic work and steps, then circle/box your final answer.

Answer 1

`(f(x + h) - f(x))/(h) = (3)/(2)`

Explanation:

Given

`f(x) = (3)/(2)x`

Required

Calculate
`(f(x + h) - f(x))/(h)`

First, we calculate f(x + h)

`f(x) = (3)/(2)x`

`f(x + h) = (3)/(2)(x + h)`

`f(x + h) = (3)/(2)x + (3)/(2)h\\`

The equation becomes:

`(f(x + h) - f(x))/(h)`

`(f(x + h) - f(x))/(h) = ((3)/(2)x + (3)/(2)h - (3)/(2)x)/(h)`

`(f(x + h) - f(x))/(h) = ((3)/(2)x - (3)/(2)x+ (3)/(2)h)/(h)`

`(f(x + h) - f(x))/(h) = ((3)/(2)h)/(h)`

`(f(x + h) - f(x))/(h) = (3)/(2)`