Español | Português
  1. Home
  2. Calculators
  3. Calculators: Calculus I
  4. Calculus Calculator

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.

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.

Your Input

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

Answer

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.