Problem 87 - Precalculus Essentials

Question

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=6$$

Step-by-Step Solution

Answer

The difference quotient for the function \(f(x) = 6\) is 0.

Step 1: Define the function

The given function is \(f(x) = 6\). We will use this function to find the difference quotient.

Step 2: Find \(f(x + h)\)

First, we find the value of the function at \(x + h\). For the function \(f(x) = 6\), \(f(x + h)\) will also be \(6\), as a constant function is always the same value, regardless of the input.

Step 3: Substitute values into the formula

Substitute \(f(x + h)\) and \(f(x)\) into the difference quotient formula, and simplify. So we get:\(\frac{f(x+h)-f(x)}{h} = \frac{6 - 6}{h} = \frac{0}{h} = 0\)