Derivatives : Point of Horizontal Tangent and Derivative at a Point

Consider the curve given by x^2+4y^2 = 7 + 3xy

a) Show that there is a point P with x-coordinate 3 at which the line tangent to the curve at P is horizontal. Find the y-coordinate of P.

b) Find the value of d^2*y/d*x^2 at the point P found in part a).

Solution Summary

The Point of a Horizontal Tangent and Derivative at a Point are found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

... Since the slope of the tangent is the derivative of the function at that point, the points where the derivative is zero will have an horizontal tangent. ...

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