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Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 5 + 4x – x2,
f(3 + h) – f(3)
h
1-1-2h-h² x
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Please try again. To evaluate f(a + h), replace x by (a + h) in the expression for f(x). Substitute this
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substituting (3+h) into the equation by replacing (3+h) where there is a x value we can get the quotient. Then repla

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sqdancefan

Answer:

  -2-h

Step-by-step explanation:

It doesn't hurt to follow directions.

  [tex]q=\dfrac{f(3+h)-f(3)}{h}=\dfrac{(5 +4(3+h)-(3+h)^2)-(5 +4(3)-(3)^2)}{h}\\\\=\dfrac{5-5+4(3+h-3)-((3+h)^2-3^2)}{h}=\dfrac{4h-(6h+h^2)}{h}\\\\=\dfrac{-2h-h^2}{h}=\boxed{-2-h}[/tex]

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Steps: substitute 3+h and 3 for x in the definition of f(x) and simplify the result.

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