Questions: Find the difference quotient (f(x+h)-f(x))/h, where h ≠ 0, for the function below.
f(x)=4x^2-2x+1
Simplify your answer as much as possible.
(f(x+h)-f(x))/h=
Transcript text: Find the difference quotient $\frac{f(x+h)-f(x)}{h}$, where $h \neq 0$, for the function below.
\[
f(x)=4 x^{2}-2 x+1
\]
Simplify your answer as much as possible.
\[
\frac{f(x+h)-f(x)}{h}=
\]
Solution
Solution Steps
To find the difference quotient \(\frac{f(x+h)-f(x)}{h}\) for the function \(f(x) = 4x^2 - 2x + 1\), follow these steps:
Substitute \(x + h\) into the function to find \(f(x + h)\).
Calculate \(f(x + h) - f(x)\).
Divide the result by \(h\).
Simplify the expression as much as possible.
Step 1: Define the Function
We start with the function given by
\[
f(x) = 4x^2 - 2x + 1.
\]