Find f(a + h) - f(a) for the function. Simplify your answer. f(x)=x^2-9x+3. I'm not exactly sure how to go about this...
first understand what \[f(a+h)\] means. it means replace x everywhere you see it by \[a+h\] so you get \[f(a+h)=(a+h)^2-9(a+h)+3\]
and of course \[f(a)=a^2-9a+3\]
so \[f(a+h)-f(a)=(a+h)^2-9(a+h)+3-(a^2-9a+3)\] and it is algebra from here on in
a bunch of algebra in fact \[a^2+2ah+h^2-9a-9h+3-a^2+9a-3\] now the usual miracle occurs, everything without an h in it goes away and you get \[2ah-9h+h^2\]
I see now. I was forgetting how to start this type of problem, but right after your first post I realized what I had to do. Thanks a ton!
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