Enter your keyword

Difference Quotient Formula

In single-variable calculus, the difference quotient is usually the name for the expression, which taken to the limit when h approaches 0, gives the derivative of the function f. Difference Quotient Formula is used to find the slope of the line that passes through two points. It is also used in the definition of the derivative.

Difference Quotient Formula

\[\LARGE \frac{f(x+h)-f(x)}{h}\]

Solved Examples

Question 1:Find the difference quotient of function f defined by $f(x) = 2x + 5$

Solution:Step 1: Calculate $f(x + h)$. $f(x + h) = 2(x + h) + 5$

Step 2: Substitute $f(x + h)$ and $f(x)$ in the definition of the difference quotient by their expressions

$\frac{[f(x+h)-f(x)]}{h}$
$\frac{[2(x+h)+5-(2x+5)]}{h}$

Step 3: Simplify the above expression.
$\frac{2h}{h}$
$=2$

Related Links
Graphs Of Trigonometric Functions FormulaCube Formula
Centroid FormulaMagnetic Field In A Solenoid Formula
Cylinder FormulaThermodynamics Formulas
Trapezoidal Rule FormulaVolume Of A Pyramid Formula
Vector Projection FormulaStopping Distance Formula
Byjus Formulas