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Find the formula for the slope of the tangent for the following function  F (x)=2/(x+7) 

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aquaneos | Student, Grade 9 | eNotes Newbie

Posted April 25, 2013 at 2:28 PM via web

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Find the formula for the slope of the tangent for the following function 

F (x)=2/(x+7) 

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 25, 2013 at 3:34 PM (Answer #1)

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You need to evaluate the slope of tangent line to the graph of function, at a given point, hence, since the point is not specified, you only could differentiate the function with respect to x, such that:

`f'(x) = (2'(x + 7) - 2*(x + 7)')/((x + 7)^2)`

`f'(x) = -2/((x + 7)^2)`

Supposing that the point is `A(x_A,y_A)` , the slope of tangent line is the following:

`m = f'(x_A) = -2/(x_A + 7)^2`

Hence, evaluating the slope of tangent line, at the point `(x_A,y_A)` , yields` m = f'(x_A) = -2/(x_A + 7)^2.`

 

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