# Help w/ the difference quotient

• EL ALEM
In summary, the difference quotient is a mathematical expression used to calculate the average rate of change of a function over a given interval. It is found by substituting the interval length (h) into the formula (f(x+h)-f(x))/h and plugging in the values of the function at x and x+h. The purpose of using the difference quotient is to understand the behavior of a function and make predictions about its future values. It can be used for any type of function and is related to the derivative as the interval length approaches 0.
EL ALEM

## Homework Statement

Show that if f(x)=sinx then (f(x+h)-f(x))/h=((sin(h/2))/(h/2))(cos(x+h/2)

## Homework Equations

Trig identities, possibly the half angle formulas?

## The Attempt at a Solution

(f(x+h)-f(x))/h
= (f(x+ h/2 + h/2)-f(x))/(h/2 + h/2)
= (sin(x+ h/2 + h/2)-sin(x))/(h/2 + h/2)
im stuck after this, don't know what to do..

Ok so I used the sum to product identity and ended up w/ this

(2sin(h/2)cos((2x+h)/2))/h

not sure how to simplify it further

NM got it.

Last edited:

## 1. What is the difference quotient?

The difference quotient is a mathematical expression used to calculate the average rate of change of a function over a given interval. It is represented by (f(x+h)-f(x))/h, where h is the interval length and f(x) is the function.

## 2. How do you find the difference quotient?

To find the difference quotient, you need to substitute the given interval length (h) into the formula (f(x+h)-f(x))/h. Then, plug in the values of the function at x and x+h to calculate the average rate of change.

## 3. What is the purpose of using the difference quotient?

The difference quotient is used to find the average rate of change of a function over a specific interval. This can help in understanding the behavior of a function and making predictions about its future values.

## 4. Can the difference quotient be used for any type of function?

Yes, the difference quotient can be used for any type of function, including linear, quadratic, exponential, and trigonometric functions. It is a general formula that can be applied to any function.

## 5. How is the difference quotient related to the derivative?

The difference quotient is the basic concept behind the definition of a derivative. It is used to find the slope of a function at a specific point, which is the same as the value of the derivative at that point. As the interval length (h) approaches 0, the difference quotient approaches the derivative of the function.

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