Question

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

Answer 1

-2-h

Explanation:

It doesn't hurt to follow directions.

`q=(f(3+h)-f(3))/(h)=((5 +4(3+h)-(3+h)^2)-(5 +4(3)-(3)^2))/(h)\\\\=(5-5+4(3+h-3)-((3+h)^2-3^2))/(h)=(4h-(6h+h^2))/(h)\\\\=(-2h-h^2)/(h)=\boxed{-2-h}`

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