SOLUTION: Given that f(x)=4/x+2, find the difference quotient f(x+h)-f(x)/h using the following steps. Be sure to simplify at every step and combine rational expressions. You don’t need to e
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-> SOLUTION: Given that f(x)=4/x+2, find the difference quotient f(x+h)-f(x)/h using the following steps. Be sure to simplify at every step and combine rational expressions. You don’t need to e
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Question 1097310: Given that f(x)=4/x+2, find the difference quotient f(x+h)-f(x)/h using the following steps. Be sure to simplify at every step and combine rational expressions. You don’t need to expand (multiply though) the common denominator for the second and third parts.
(a) find f(x+h)=
(b) find f(x+h)-f(x)=
(c) find f(x+h)-f(x)/h= Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! f(x+h)-f(x)/h gives us the first derivative of a given function as h approaches 0
:
we are given f(x) = (4/x) + 2
:
a) (4/(x+h)) + 2
:
b) (4/(x+h)) + 2 - (4/x) - 2 =
:
4/(x+h) - (4/x) =
:
4x - 4(x+h) / x(x+h) =
:
4x -4x -4h / x(x+h) =
:
-4h / x(x+h)
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c) (-4h / x(x+h)) / h =
:
-4h / xh(x+h) =
:
-4 / x^2 + xh
:
as h approaches 0, we have -4/x^2
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