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Nov 21, 2023 · The formula for the difference quotient is: DQ = f (x+h) - f (x) / h (where h is the denominator). If evaluating the derivative using the difference quotient, evaluate the DQ by...
- What Is The Difference Quotient Formula?
- Difference Quotient Formula Derivation
- Examples Using Difference Quotient Formula
By seeing the name, "difference quotient formula", are you able to recollect something? The words "difference" and "quotient" are giving the feel of the slope formula. Yes, the difference quotient formula gives the slope of a secant line that is drawn to a curve. What is a secant line? A secant line of a curve is a line that passes through any two ...
Let us consider a function y = f(x) and let a secant line passes through two points of the curve (x, f(x)) and (x + h, f(x + h)). Thus using the slope formula, the slope of the secant line is, [ f(x + h) - f(x) ] / [ (x + h) - x] = [ f(x + h) - f(x) ] / h [Since the slope of any straight line = change in y/ change in x.) This is nothing but the dif...
Example 1: Find the difference quotient of the function f(x) = 3x - 5. Solution: Using the difference quotient formula, Difference quotient of f(x) = [ f(x + h) - f(x) ] / h = [ (3(x + h) - 5) - (3x - 5) ] / h = [ 3x + 3h - 5 - 3x + 5 ] / h = [ 3h ] / h = 3 Answer: The difference quotient of f(x) is 3. Example 2 : Find the derivative of f(x) = 2x2-...
Jul 10, 2023 · Definition: Given a function f, we refer to f(a + h) − f(a) h as the difference quotient. More will be said about the difference quotient in the coming days but for now, allow us to compute a few more difference quotients.
The slope \( m \) of the secant line may be calculated as follows: \[ m = \dfrac{f (x + h) - f(x)}{(x + h) - x} \] Simplify the denominator to obtain \[ m = \dfrac{f (x + h) - f(x)}{h} \] The slope \( m \) is called the difference quotient. It is a very important concept in calculus where it is used to define the derivative of function \( f ...
The Difference Quotient. This video gives the formula for the difference quotient (the subtraction fraction) and do a couple examples of finding it for different functions. Examples: a) Let f (x) = 2x - 5; find f (x+h) - f (x) b) Let f (x) = 3x + 2; find the difference quotient: (f (x+h) - f (x))/h. Show Video Lesson. The Difference Quotient.
The difference quotient is a new expression created from a template and a given function formula. The template for the difference quotient of the function y = f(x) y = f ( x) is. f(x+h)−f(x) h. f ( x + h) − f ( x) h. It will be discussed later why this is an important expression.
