SOLUTION: Find and simplify the difference quotient f(x+h)-f(x)/h for the function f(x) = x^2 + 3.

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Question 1113382: Find and simplify the difference quotient f(x+h)-f(x)/h for the function f(x) = x^2 + 3.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
You most certainly wanted to ask for ++%28f%28x%2Bh%29-f%28x%29%29%2Fh++ and not +++f%28x%2Bh%29-f%28x%29%2Fh++
(Use paren's)
—

= +%28+%28%28x%5E2+%2B+2hx+%2B+h%5E2%29+%2B+3%29+-+%28x%5E2+%2B+3%29%29+%2F+h+
= +%28+x%5E2+%2B+2hx+%2B+h%5E2+%2B+3++-+x%5E2+-+3%29+%2F+h+
=
= ++%28+++2hx+%2B+h%5E2+%29+%2F+h+
= ++highlight+%28+2x+%2B+h%29+
——
Just some seeds for your mathematical future:
In Calculus I, you will learn about the derivative (= rate of change) of a function. This problem is leading up to the basis for the derivative, where one finds the limit of (f(x+h)-f(x))/h as h—>0 (here it would be 2x because h vanishes as h—>0).