Question

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

A) (7/2)
B) 1
C) h
D) (7h/2)

Answer 1

The difference quotient for the function f(x) = (7/2)x - 16 for all nonzero values of h is (7/2).

Step-by-step explanation:

The student's question asks for the difference quotient for the function f(x) = (7/2)x - 16 when h is nonzero. The difference quotient is defined as (f(x + h) - f(x))/h. The difference quotient for the given function is calculated as follows:

1. Plug x + h into the function: f(x + h) = (7/2)(x + h) - 16.
2. Expand the function: f(x + h) = (7/2)x + (7/2)h - 16.
3. Subtract the original function f(x): (f(x + h) - f(x)) = [(7/2)x + (7/2)h - 16] - [(7/2)x - 16].
4. Simplify the expression: (f(x + h) - f(x)) = (7/2)h.
5. Divide by h: ((f(x + h) - f(x))/h) = (7/2).

Therefore, the difference quotient for all nonzero values of h is (7/2), which is option A.