Technical Calculator

Difference Quotient Calculator

Enter the function, choose the variable, and click on the “Calculate” button to calculate the difference quotient.

Home > Math > Difference Quotient Calculator
keyboard

add to favorites Add to favorites

distinction Quotient Calculator

Use this distinction quotient calculator to locate how much a function modifications on common over a selected c language. Our device presentations stepwise calculations to degree the slope of the secant line which passes via two points.

what is the distinction Quotient?

"distinction quotient is a mathematical expression used to degree the slope of the secant line among the two one-of-a-kind factors on the graph of a feature."

In easy words, the distinction quotient measures the charge of trade of a function f(x) for x in a given c language [x, x + h].

Distinction Quotient method:

The difference quotient equation measures the approximated shape of the spinoff as:

f(x) = f(x + h) – f(x) h

Where:

  • f(x) represents the function of “x”
  • h suggests the interval length
  • x + h is the increment within the input

The difference quotient components affords an approximation of a characteristic's derivative.

How to Calculate distinction Quotient?

Observe these steps to decide difference quotients:

  • pick out the characteristic: determine the characteristic f(x)
  • compare f(x+h): placed (x+h) for x inside the characteristic f(x)
  • locate the distinction: Subtract f(x) from f(x+h)
  • Divide via h: Divide the difference by means of h

Example:

Find the difference quotient for the following function:

F(x) = 3x3 + 5x

Solution:

To find f(x + h), substitute x + h for x:

f(x + h) = 3(x + h)3 + 5(x + h)

Then,

= ((x + h)3 + 5(x + h)) – (3x3 + 5x) h

= (x + h)3 + 5x + 5h – 3x3 – 5x h

= 3h(x2 + 2xh + h2) + 5h h

f(x) = 3x3 + 5x = 3h(x2 + 2xh + h2) + 5h

Thus, the difference quotient for f(x) = 3x3 + 5x is \( 3h(x^2 + 2xh + h^2) + 5h \). For quick results, use our simplified difference quotient calculator.