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

Answer:

$\frac{f(x + h) - f(x)}{h} = \frac{3}{2}$

Step-by-step explanation:

Given

$f(x) = \frac{3}{2}x$

Required

Calculate $\frac{f(x + h) - f(x)}{h}$

First, we calculate f(x + h)

$f(x) = \frac{3}{2}x$

$f(x + h) = \frac{3}{2}(x + h)$

$f(x + h) = \frac{3}{2}x + \frac{3}{2}h$

The equation becomes:

$\frac{f(x + h) - f(x)}{h}$

$\frac{f(x + h) - f(x)}{h} = \frac{\frac{3}{2}x + \frac{3}{2}h - \frac{3}{2}x}{h}$

$\frac{f(x + h) - f(x)}{h} = \frac{\frac{3}{2}x - \frac{3}{2}x+ \frac{3}{2}h}{h}$

$\frac{f(x + h) - f(x)}{h} = \frac{\frac{3}{2}h}{h}$

$\frac{f(x + h) - f(x)}{h} = \frac{3}{2}$