Find f(a), f(a + h), and the difference quotient f(a + h) − f(a) h , where h

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Find 
f(a), f(a + h),
 and the difference quotient 
f(a + h) − f(a)
h
,
 where h ≠ 0.

f(x) = 5 − 3x + 4x2

f(a) =

f(a + h)

=
f(a + h) − f(a)
h
Jun 28th, 2015

Thank you for the opportunity to help you with your question!

f(x) = 5 − 3x + 4x2

f(a) = 5 − 3a + 4a^2

f(a+h) = 5 − 3(a+h) + 4(a+h)^2 = 5 − 3a-3h + 4a^2+4h^2+ 8ah

[f(a+h) - f(a)]/h =  (5 − 3a-3h + 4a^2+4h^2+ 8ah - 5+ 3a-4a^2 ) /h

                        = (-3h + 4h^2 +8ah)/h = 4h+8a-3


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Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 28th, 2015

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