Question
Asked Jul 4, 2019
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Find the difference quotient and simplify your answer.

f(x) = 5x – x2,  f(6 + h)-f(6)/h  , h ≠ 0

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Expert Answer

Step 1

To find the difference quotient.

The given function is f(x) = 5x – x2.

Find f(6+h) and f(6) .

=5(6+h)-(6+h)
=30+5h-(36+12h +h2
30+5h-36-12h-h
f(6+h)
=-h-7h-6
=5(6)-(6
f(6)
30-36
=-6
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=5(6+h)-(6+h) =30+5h-(36+12h +h2 30+5h-36-12h-h f(6+h) =-h-7h-6 =5(6)-(6 f(6) 30-36 =-6

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Step 2

To find the difference quoti...

--7h-6-(-6)
f(6+h)-f(6)
h
-h2-7h-6+6
h
-h-7h
h
h(-h-7)
h
=-h-7
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--7h-6-(-6) f(6+h)-f(6) h -h2-7h-6+6 h -h-7h h h(-h-7) h =-h-7

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