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#?
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