Compute the difference quotient \( \frac{f(x+h)-f(x)}{h} \) for the function given below.

To compute the difference quotient \( \frac{f(x+h)-f(x)}{h} \) for a function \( f(x) \), you would first need to know the specific form of \( f(x) \). For instance, if \( f(x) = x^2 \), we would find: 1. **Calculate \( f(x+h) \)**: \[ f(x+h) = (x+h)^2 = x^2 + 2xh + h^2 \] 2. **Compute \( f(x+h) - f(x) \)**: \[ f(x+h) - f(x) = (x^2 + 2xh + h^2) - x^2 = 2xh + h^2 \] 3. **Form the difference quotient**: \[ \frac{f(x+h) - f(x)}{h} = \frac{2xh + h^2}{h} = 2x + h \] So, the difference quotient for \( f(x) = x^2 \) simplifies nicely to \( 2x + h \). For other functions, you would follow a similar process of substituting \( x + h \) into the function, calculating the difference, and then simplifying the resulting expression!