SOLUTION: 1) Find the difference quotient and simplify your answer. f(x) = x2 − x + 8, f(4 + h) − f(4)/h, h ≠ 0 2) Find the difference quotient and simplify your a

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Question 896991: 1) Find the difference quotient and simplify your answer.
f(x) = x2 − x + 8, f(4 + h) − f(4)/h, h ≠ 0


2) Find the difference quotient and simplify your answer.
f(x) = 7x2 − 8x, f(x + h) − f(x)/h, h ≠ 0




Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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problem number 1:

f(x) = x2 − x + 8, f(4 + h) − f(4)/h, h ≠ 0

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

f(4) = 4^2 - 4 + 8 = 16 - 4 + 8 which becomes:

f(4) = 16 + 4 which becomes:

f(4) = 20

f(4 + h) = (4+h)^2 - (4+h) + 8 which becomes:

f(4 + h) = 16 + 8h + h^2 - 4 - h + 8 which becomes:

f(4 + h) = h^2 + 7h + 20

f(4+h) - f(4) = h^2 + 7h + 20 - 20 which becomes:

f(4+h) - f(4) = h^2 + 7h

(f(4+h) - f(4)) / h = (h^2 + 7h) / h

when h is not equal to 0, this can be simplified to:

(f(4+h) - f(4)) / h = h + 7

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problem number 2:

f(x) = 7x2 − 8x, f(x + h) − f(x)/h, h ≠ 0

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f(x) = 7x^2 - 8x

f(x+h) = 7(x+h)^2 - 8(x+h) which becomes:

f(x+h) = 7(x^2 + 2hx + h^2) - 8x - 8h which becomes:

f(x+h) = 7x^2 + 14hx + 7h^2 - 8x - 8h.

f(x+h) - f(h) = 7x^2 + 14hx + 7h^2 - 8x - 8h - (7x^2 - 8x) which becomes:

f(x+h) - f(h) = 7x^2 + 14hx + 7h^2 - 8x - 8h - 7x^2 + 8x which becomes:

f(x+h) - f(h) = 7h^2 + 14hx - 8h

the 7x^2 and minus 7x^2 cancel out and the 8x and minus 8x also cancel out.

(f(x+h) - f(x)) / h = (7h^2 + 14hx - 8h) / h

when h is not equal to 0, you can simplify this to get:

(f(x+h) - f(x)) / h = 7h + 14x - 8
















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