SOLUTION: Please help with this problem: Find the indicated difference quotient and simplify answer. Given f(x) = x^2 = 5x + 1 find f(5 + h)

SOLUTION: Please help with this problem: Find the indicated difference quotient and simplify answer. Given f(x) = x^2 = 5x + 1 find f(5 + h) - f(5) over h what I did: 1. f(5+h)

Question 16724: Please help with this problem:
Find the indicated difference quotient and simplify answer.
Given f(x) = x^2 = 5x + 1
find f(5 + h) - f(5) over h
what I did:
1. f(5+h) = (5+h)^2 + 5(5+h) +1
=(5+h)(5+h) + 5(5+h) +1
=25 +5h +5h +h^2 +25 +5h + 1
=51 + 15h +h^2
2. f(5+h) - f(5) = 51 + 15h + h^2 - 5^2 + 5(5) + 1
= 51 + 15h + h^2 - 25 + 25 + 1
= 52 + 15h + h2
3. f(5+h) - f(5) over h = 52 + 15h + h^2 over h
The teacher's answer is 15 + h
Where did I go wrong?
Please help!
Thanks,
Sandy
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
In step 2, you made the most common error in this type of problem. When you do f(5+h) - f(5), be sure to minus the quantity of f(5)!!

It should look like this with extra parentheses added:
f(5+h) - f(5) = 51 + 15h + h^2 - (5^2 + 5(5) + 1)
= 51 + 15h + h^2 - (25 + 25 + 1)
= 15h + h2
3. f(5+h) - f(5) over h = (15h + h^2) over h, which comes out to

The teacher's answer which is 15 + h

R^2 at SCC
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