Question

given the following function, determine the difference quotient, \\( \frac { f ( x + h ) - f ( x ) } { h } \\).
\\( f ( x ) = 4 x - 1 \\)

Explanation:

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

Substitute \(x+h\) into \(f(x)\): \(f(x + h)=4(x + h)-1=4x+4h - 1\)

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

\(f(x + h)-f(x)=(4x + 4h-1)-(4x - 1)\)
\(=4x+4h - 1-4x + 1\)
\(=4h\)

Step3: Compute \(\frac{f(x + h)-f(x)}{h}\)

\(\frac{f(x + h)-f(x)}{h}=\frac{4h}{h}\)

Answer:

\(4\)