MAIMOM Posted September 27, 2012 Share Posted September 27, 2012 (edited) My DD brought me this problem and says she is stumped and has no idea how they got the answer. Can anyone here help us? Directions: Find the difference quotient and simplify your answer f(x) = x squared -x +1, f(2+h0 -f(2), {this line is over h} h does not equal 0 :confused: stumped more than my DD Edited September 27, 2012 by MAIMOM Quote Link to comment Share on other sites More sharing options...

kiana Posted September 27, 2012 Share Posted September 27, 2012 note: x^2 means x squared. f(2+h) means that you're putting (2+h) into the function instead of x. So wherever you see an x, change it to (2+h). So f(2+h) = (2+h)^2 - (2+h) + 1. We know that f(2) = 4-2+1 = 3, so our difference quotient is: ((2+h)^2 - (2+h) + 1) - 3 -------------------------- h When we go to simplify this, we must be careful to square (2+h) properly. It is a *very* common mistake to try to write '4+h^2' instead ... watch out for this! (2+h)^2 = 2^2 + 2*2*h + h^2 = 4 + 4h + h^2. We also have to be careful to distribute the minus sign through the parentheses. So we get: (4 + 4h + h^2 - 2 - h + 1) -3 ---------------------------- h After combining like terms, we get: 3h + h^2 --------- h Another REALLY COMMON error to watch out for here is improper cancellation. We can't just start crossing off h's. We have to factor first. After factoring, we get: h(3+h) ------ h And then we can cancel the h's to get 3+h, which hopefully is the answer she was looking for; if not, there may be a typo in the answer book. Quote Link to comment Share on other sites More sharing options...

MAIMOM Posted September 27, 2012 Author Share Posted September 27, 2012 note: x^2 means x squared. f(2+h) means that you're putting (2+h) into the function instead of x. So wherever you see an x, change it to (2+h). So f(2+h) = (2+h)^2 - (2+h) + 1. We know that f(2) = 4-2+1 = 3, so our difference quotient is: ((2+h)^2 - (2+h) + 1) - 3 -------------------------- h When we go to simplify this, we must be careful to square (2+h) properly. It is a *very* common mistake to try to write '4+h^2' instead ... watch out for this! (2+h)^2 = 2^2 + 2*2*h + h^2 = 4 + 4h + h^2. We also have to be careful to distribute the minus sign through the parentheses. So we get: (4 + 4h + h^2 - 2 - h + 1) -3 ---------------------------- h After combining like terms, we get: 3h + h^2 --------- h Another REALLY COMMON error to watch out for here is improper cancellation. We can't just start crossing off h's. We have to factor first. After factoring, we get: h(3+h) ------ h And then we can cancel the h's to get 3+h, which hopefully is the answer she was looking for; if not, there may be a typo in the answer book. Thank you so much. I love this forum! HUGS Kiana for your help!:grouphug: Quote Link to comment Share on other sites More sharing options...

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