One of the most important topics in Calculus is the difference quotient. That's why you see it appear so often in algebra and pre-calculus. You probably have seen it before, you may have seen it many times before, but in Section 2.8 we used the (familiar?) difference quotient formulaf(x+h)f(x)h

As you saw in the textbook/homework, there are several components to the difference quotient you need to be careful about. For this discussion, consider the following difference quotient problem and theincorrectsolution that follows.

Problem: Find the difference quotient forf(x)=x2+x+2

INCORRECT SOLUTION

f(x)=x2+x+2

so that meansf(x+h)=(x+h)2+x+2=x2+h2+x+2

andf(x+h)f(x)=x2+h2+x+2x2+x+2=h2+2x+4

and finallyf(x+h)f(x)h=h2+2x+4h=h+2x+4

Post a reply pointing out as many things as you can find that areWRONGabout the above work.

(There are at least 4 things wrong with it, but maybe you can find even more!)

Note: You do NOT need to find the correct answer to the problem. Be sure to point out what isWRONGwith the above work, don't just say "The correct answer should be ..."