Difference Quotient Formula

About Difference Quotient Formula

The difference quotient is the name for the statement in single-variable calculus that, when taken to the limit when h approaches 0, produces the derivative of the function f. The slope of a line passing through two locations is calculated using the Difference Quotient Formula. It is also used in the derivative definition. Get the list of Maths Formulas. 

Difference Quotient Formula

$\frac{\mathrm{f}(\mathrm{x}+\mathrm{h})-\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{h}}$

Solved Example of Difference Quotient Formula

Example: Find the distinction the quotient of the function f, as defined by

Sol: Step 1: Calculate

i.e., = 2(x + h) + 5 = 2x + 2h + 5

Step 2: Substitute and in the formula of the difference quotient.

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

Step 3: Simplifying the above expression,= 2h/h = 2

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