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find the points at which the graph of the equation

0 votes
4x^2 + y^2 -8x +4y +4=0 has a vertical or horizontal tangent line
asked Sep 24, 2014 in CALCULUS by anonymous

1 Answer

0 votes

The curve equation is image

Recall that slope of the horizontal line is zero and slope of the vertical line is undefined.

The curve has horizontal tangent lines.

Tangent line slope is y'.

image

Differentiate implicitly.

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image

Equate the y' = 0.

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Substitute x = 1 in the curve and solve for y.

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image

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Tangent points are (1, 0) and (1, - 4).

answered Sep 24, 2014 by david Expert
edited Sep 24, 2014 by david

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