# Difference Quotient Calculator

The calculator will find the difference quotient for the given function, with steps shown.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Find the difference quotient for $f{\left(x \right)} = x^{2} + 3 x + 5$.

## Solution

The difference quotient is given by $\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}$.

To find $f{\left(x + h \right)}$, plug $x + h$ instead of $x$: $f{\left(x + h \right)} = \left(x + h\right)^{2} + 3 \left(x + h\right) + 5$.

Finally, $\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(\left(x + h\right)^{2} + 3 \left(x + h\right) + 5\right) - \left(x^{2} + 3 x + 5\right)}{h} = h + 2 x + 3$.

The difference quotient for $f{\left(x \right)} = x^{2} + 3 x + 5$A is $h + 2 x + 3$A.