Question

consider the function ( f(x)=5x - 6 ).
simplify the difference quotient
( \frac{f(x + h)-f(x)}{h} )

Explanation:

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

Substitute \(x+h\) into \(f(x)=5x - 6\).
\(f(x + h)=5(x + h)-6=5x+5h - 6\)

Step2: Substitute \(f(x + h)\) and \(f(x)\) into the difference quotient

\(\frac{f(x + h)-f(x)}{h}=\frac{(5x + 5h-6)-(5x - 6)}{h}\)

Step3: Simplify the numerator

\((5x + 5h-6)-(5x - 6)=5x+5h - 6-5x + 6=5h\)

Step4: Simplify the quotient

\(\frac{5h}{h}=5\)

Answer:

\(5\)