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Math Help - slope of tangent line

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    slope of tangent line

    (a) Find the slope of the tangent line to the curve y = 9-x2 at the point whose x-coordinate is 2.


    (b) Find the equation of this tangent line in a slope-intercept form.
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    Re: slope of tangent line

    Quote Originally Posted by olemiss13 View Post
    (a) Find the slope of the tangent line to the curve y = 9-x2 at the point whose x-coordinate is 2.
    (b) Find the equation of this tangent line in a slope-intercept form.
    Slope of the tangent line = \frac{dy}{dx}
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  3. #3
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    Re: slope of tangent line

    (a) \frac{dy}{dx} = -2x. Particularly, at x = 2, \frac{dy}{dx} = -2(2) = -4. Slope is -4.

    (b) We know that the function goes through the point (2,5) (substituted x=2 into the original function). Therefore we can write in point-slope form and convert to slope-intercept form:

    y-5 = -4(x-2) \Rightarrow y = -4x + 13
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