Question

for the function $f(x) = 2x + 1$, evaluate and simplify.\\(\frac{f(x + h) - f(x)}{h}\\) =

Explanation:

Step1: Find \( f(x + h) \)

Substitute \( x + h \) into \( f(x) = 2x + 1 \), so \( f(x + h)=2(x + h)+1 = 2x+2h + 1 \).

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

Substitute \( f(x + h)=2x + 2h+1 \) and \( f(x)=2x + 1 \) into \( f(x + h)-f(x) \), we get \( (2x + 2h+1)-(2x + 1)=2x + 2h+1 - 2x - 1 = 2h \).

Step3: Divide by \( h \)

Divide \( f(x + h)-f(x)=2h \) by \( h \) (assuming \( h
eq0 \)), so \( \frac{f(x + h)-f(x)}{h}=\frac{2h}{h}=2 \).

Answer:

\( 2 \)