Solving Equations and Differentiation Exercise - Question 1

Part (a): Solving an equation and finding range of values of variables

Question 1

(a) Real variables x and y are related by the equation

ln y – ln (y + 3) + ln 4 = 2 ln x.

(i) Identify the range of values of x and y for which the expressions an either side of this equation are defined.

(ii) Determine y explicitly as a function of x, that is, identify the equation in the form y = f(x).

(b) By using implicit differentiation, present dy/dx to the curve

x3– 2xy + y2

= 1 at the point (1,2). Hence present the equation of the tangent to the curve at this point.