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

The calculator will find the difference quotient for the function $f{\left(x \right)} = x^{4} - x^{2} + 3 x$, with steps shown.

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

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

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

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