Web(a) The curve with equation $ y^2 = x^3 + 3x^2 $ is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, -2). (b) At what points does this curve have horizontal tangents? (c) Illustrate parts (a) and (b) by graphing the curve and the tangent lines on a common screen. WebJul 27, 2024 · Find an equation of the. (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 = (b) At what points does this curve have horizontal tangents? (x, y) = …
Math 2250 Exam #2 Solutions - Colorado State University
WebThe curve with equation y^2=x^3+3 x^2 y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1,-2). At what points does this curve have horizontal tangents? WebThe Tschirnhausen cubic. As an example of implicit differentiation, ... alone. For example, the tangents at the two points with x-coordinate 1 on this cubic have different slopes: At (1,2) ... Picking values for z just amounts to slicing this graph with horizontal planes, forming "contours" of the surface. The plane z=0 gives the present cubic; ... can you jump start a car with a golf cart
Chapter 3, Differentiation Rules Video Solutions, Calculus: Early ...
Web3.The curve determined by the equation y2 = x2(x + 1), pictured below, is called the Tschirnhausen cubic. At what points does this curve have a horizontal tangent line? Answer: Di erentiating implicitly, we have 2y y0= 2x(x+ 1) + x2(1): Thus, y0= 2x 2+ 2x+ x 2y = 3x2 + 2x 2y: The curve will have a horizontal tangent line only when the above is ... WebAt what points does this curve have horizontal tange; The curve with equation y^2 = x^3 + 3x^2is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). And at what points does this curve have horizontal (a) The curve with equation y^{2} = x^{3} + 3x^{2} is called the Tschirnhausen cubic. WebThe curve with the equation 2y^2=2x^3+6x^2 is called the Tschirnhausen cubic. Find the equation of the tangent line to this curve at the point (1, -2) The curve with equation y^2 = x^3 + 3x^2is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve at the point (1, 2). And at what points does this curve have horizontal bright star poem summary