Difference Quotient Examples

Difference Quotient Examples Difference quotient examples help in finding derivative of a function. Dividing the function difference from the difference of the points is called as difference quotient. This gives slope of a secant line passing through two points. The formula for finding difference quotient is (f(x + h) f(x)) / h and it is denoted by dy /dx. Problem 1: Consider a function f(x) = 2x^2 5 and x changes from 1 to 1.4. Find the value of the difference quotient in this situation. Solution: Given function isf(x) = 2x^2 5 = So f(x + h) = 2(x + h) ^2 5 = Difference Quotient for function f(x) = (f(x + h) f(x)) / h = (2(x + h) ^2 5 (2x^2 5)) / h= (2x^2 + 4xh + 2h^2 5 -2x^2 + 5)/ h = (4xh + 2h^2)/ h = 4x + 2h = Given x changes from 1 to 1.4 = So dx = 1.4 1 = 0.4. (Hence, h = 0.4) = Using x = 1 and h = 0.4 then = Difference quotient = 4x + 2h = 4(1) + 2(0.4)) = 4 + 0.8 = 4.08 = Therefore, 4.08 is the slope of secant line when x changes from 1 to 1.3 Problem 2: Consider the function f(x) = 7x 2. Find the difference quotient and find dy when dx = 2. Solution: Given function isf(x) = 7x 2 = So f(x + h) = 7(x +h) 2 = Difference Quotient for function f(x) = (f(x + h) f(x)) / h = (7(x +h) 2 (7x 2)) / h = 7 = Difference quotient is always 7 for this function. = We have dy / dx = 7 = dy = 7 * dx = 7 * 2 = 14.