# How do you find the difference quotient of #f#, that is, find #((f(x+h)-f(x))/h)#, #h != 0# for #f(x)=x^2-5x+7#?

##### 1 Answer

see explanation

#### Explanation:

If I understand the question correctly, you have to start by substituting

multiplying out, you have:

So, substitute this as the value of

...this simplifies to:

...now, since this is calculus, the inevitable next step is to find the limit of this function as h -> 0. For this, you can't have h in the denominator. But we can do a little factoring kung-fu. The equation above can be re-written:

...and the limit of this function, as h approaches 0, is :

...which is the derivative of the original function

GOOD LUCK