Question

For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?

Answer 1

It is A.

Explanation:

Just took the test

Answer 2

`(f(x + h) - f(x))/( h) = (7)/(2)`

Explanation:

Given

`f(x) = (7)/(2)x - 16`

Required

The difference quotient for h

The difference quotient is calculated as:

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

Calculate f(x + h)

`f(x) = (7)/(2)x - 16`

`f(x+h) = (7)/(2)(x+h) - 16`

`f(x+h) = (7)/(2)x+ (7)/(2)h- 16`

The numerator of
`(f(x + h) - f(x))/( h)` is:

`f(x + h) - f(x) = (7)/(2)x+ (7)/(2)h- 16 -((7)/(2)x - 16)`

`f(x + h) - f(x) = (7)/(2)x+ (7)/(2)h- 16 -(7)/(2)x + 16`

Collect like terms

`f(x + h) - f(x) = (7)/(2)x -(7)/(2)x + (7)/(2)h- 16 + 16`

`f(x + h) - f(x) = (7)/(2)h`

So, we have:

`(f(x + h) - f(x))/( h) = (7)/(2)h / h`

Rewrite as:

`(f(x + h) - f(x))/( h) = (7)/(2)h * (1)/(h)`

`(f(x + h) - f(x))/( h) = (7)/(2)`