part A. let C be a curve of points in R^2 which satisfy the equation  x^3 + xy +y^2 =3. use implicit differentiation to compute y'.

plot the curve where (y^2)-2 /(y+3) = x^3/x+4, including all interesting features. match slopes at every axis crossing with those you can calculate via implicit differentiation

Consider the function f(x) = x / x^2+9 use the function to complete the following steps:  a.) find all points where f'(x)=0 b.) find the equation of the tangent line at the point (3, 6) c.) use the quotient rule to find f'(x)

Find the slope of the tangent to the graph of f(x) = x^2 + 1 at the point (2, 5).  Use the method of finding the slope of the secant between (2, 5) and a neighboring point, and moving the neighboring point closer and closer to (2, 5).  What is important here is the method, not the answer, so show your work very clearly.  A diagram is needed, but you do not need to draw all your secant lines if that becomes difficult.