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

Difference quotient for $$$f{\left(x \right)} = 5 x^{2} - 3$$$

The calculator will find the difference quotient for the function $$$f{\left(x \right)} = 5 x^{2} - 3$$$, 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 $$$f{\left(x \right)} = 5 x^{2} - 3$$$.

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

Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(5 \left(x + h\right)^{2} - 3\right) - \left(5 x^{2} - 3\right)}{h} = 5 h + 10 x$$$.

Answer

The difference quotient for $$$f{\left(x \right)} = 5 x^{2} - 3$$$A is $$$5 h + 10 x$$$A.