A) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). y = Correct: Your answer is correct. (b) At what points does this curve have horizontal tangents? (x, y) = -2 Incorrect: Your answer is incorrect. (smaller y-value) (x, y) = 2 Incorrect: Your answer is incorrect. (larger y-value)

Tangent at (1,2) has value . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

At (1, 2), tangent line is,

To find point of intersection of horizontal tangent we have to do,

Thus,

At x=0, y=0

but snce,

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

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