Answer to Question #16307 in Calculus for hsd

Question

The curve C is given by x^2 - 2y^2 = 4:
(a) Which parts of C can be described as graphs of functions y(x)? Determine these functions y(x) and state their domains.
(b) Sketch the curve C.
(c) Determine the equations of the tangent lines to C at the points (-4, √6), (-4,-√6) and (-2, 0).
(d) Compute dy/dx , d^(2)y/dx^(2) and d^(3)y/ dx^(3) at the point (4,√6).
(e) Determine all points of C at which dy/dx is not defined and explain why this is the case.