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find the equation of the tangent line to the graph of  at `x^2`  ( -3 , 9 )``

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user7230927 | Honors

Posted June 5, 2013 at 5:12 PM via web

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find the equation of the tangent line to the graph of  at `x^2`  ( -3 , 9 )``

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted June 5, 2013 at 5:33 PM (Answer #1)

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You need to find the equation of tangent line to the curve `y = x^2` , at the point `(-3,9)` , such that:

`y - 9 = (dy)/(dx)|_(x=-3)(x - (-3))`

You need to differentiate the function with respect to x, such that:

`(dy)/(dx) = (d(x^2))/(dx) => (dy)/(dx) = 2x`

You need to evaluate derivative of the function at `x = -3` , such that:

`(dy)/(dx)|_(x=-3) = 2*(-3) = -6`

`y - 9 = -6(x+3) => y = 9 - 6x - 18 => y = -6x - 9`

Hence, evaluating the equation of the tangent line, to the given curve, at the point `(-3,9)` , yields `y = -6x - 9.`

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