If f(x)=3x^3-x^2+8x-1, find f(a+h)-f(a) / h
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If f(x)=3x^3-x^2+8x-1, find f(a+h)-f(a) / h

[From: ] [author: ] [Date: 12-04-09] [Hit: ]
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My choices are:

a. 6a 2 + 9ah + 9h 2 - 2a – h
b. 9a 2 - 9ah + 3h 2 - 2a - h + 8
c. 3a 2 + 3ah + 3h 2 - 2a - h + 8
d. 9a 2 + 9ah + 3h 2 - 2a - h + 8
e. 3a 2 + 9ah + h 2 - 2a + h

-
f(x) = 3x^3 - x^2 + 8x - 1

f(a + h) = 3(a² + 2ah + h²)(a + h) - (a + h)² + 8a + 8h - 1 = 3(a^3 + 3a²h + 3ah² + h^3) - a² - 2ah - h² + 8a + 8h - 1

f(a) = 3a^3 - a^2 + 8a - 1

f(a + h) - f(a) = 3a^3 + 9a²h + 9ah² + 3h^3 - a² - 2ah - h² + 8a + 8h - 1 - 3a^3 + a^2 - 8a + 1

= 9a²h + 9ah² + 3h^3 - 2ah - h² + 8h

[f(a + h) - f(a)]/h = 9a² + 9ah + 3h² - 2a - h + 8
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keywords: If,find,If f(x)=3x^3-x^2+8x-1, find f(a+h)-f(a) / h
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