Difference quotient for $$$f{\left(x \right)} = 3 x^{2} - 4 x$$$

Find the difference quotient for $$$f{\left(x \right)} = 3 x^{2} - 4 x$$$.

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 $$$x$$$: $$$f{\left(x + h \right)} = 3 \left(x + h\right)^{2} - 4 \left(x + h\right)$$$.

Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(3 \left(x + h\right)^{2} - 4 \left(x + h\right)\right) - \left(3 x^{2} - 4 x\right)}{h} = 3 h + 6 x - 4$$$.

The difference quotient for $$$f{\left(x \right)} = 3 x^{2} - 4 x$$$A is $$$3 h + 6 x - 4$$$A.