Difference Quotient Calculator

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

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.