The difference quotient (f(x+h)-f(x))/h

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Question from helen, a student:

f(x)=x^2-x+4
Find the difference quotient of f, f(x+h)-f(x)/h, h does not equal 0,

Helen,

As "h" is an indeterminate, not a number, it is unnecessary to specify that it doesn't equal 0.

First find (and expand) f(x+h), that is, (x+h)² - (x+h) +4.

Now subtract x² -x + 4 (and simplify).

Now divide by h (and simplify.) You will find that what you have after the last step will divide by h since f is a polynomial. When you get to calculus (which is what this is in preparation for!) you will learn how to use limits to deal with other functions.

Good Hunting!
-RD

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