Question

find the difference quotient of f; that is, find $\frac{f(x + h)-f(x)}{h}$, h $
eq$ 0, for the following function. f(x)=2x + 3 $\frac{f(x + h)-f(x)}{h}=square$ (simplify your answer.)

Explanation:

Step1: Find f(x + h)

Substitute \(x+h\) into \(f(x)\):
\[f(x + h)=2(x + h)+3=2x+2h + 3\]

Step2: Calculate f(x + h)-f(x)

\[f(x + h)-f(x)=(2x + 2h+3)-(2x + 3)=2x+2h + 3-2x - 3=2h\]

Step3: Find the difference quotient

\[\frac{f(x + h)-f(x)}{h}=\frac{2h}{h}=2\]

Answer:

2