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# Find the difference quotient of f; that is, find f(x+h)-f(x) / h ,h ≠ 0 . Be sure to simplify.?

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- llafferLv 78 months ago
You have:

f(x) = x² - 9x + 2

And asked to solve for:

[f(x + h) - f(x)] / h

We have f(x) already, so we need to find f(x + h):

f(x) = x² - 9x + 2

f(x + h) = (x + h)² - 9(x + h) + 2

Simplify:

f(x + h) = x² + 2hx + h² - 9x - 9h + 2

Now we can substitute both expressions into the main expression and simplify:

[f(x + h) - f(x)] / h

[(x² + 2hx + h² - 9x - 9h + 2) - (x² - 9x + 2)] / h

(x² + 2hx + h² - 9x - 9h + 2 - x² + 9x - 2) / h

Cancel out what can be:

(2hx + h² - 9h) / h

Factor out the h and cancel with the denominator:

h(2x + h - 9) / h

2x + h - 9

- ted sLv 78 months ago
( x + h)² - x² - ( 9x + 9h - 9 x ) + ( 2 - 2 ) = 2 h x + h² - 9 h = h [ 2x + h - 9 ] ===> answer is 2x - 6 + h

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