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
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