Mathematical Muscle-building:

Implicit Differentiation

(1)Suppose x + y = 10
(a) Find dy/dx
(b) What is the slope of the tangent to this curve which passes through (36,16)?
 [Confirm first that the curve does, in fact, pass through this point].
(c) Find an equation for this line.

(2) Consider the equation y2=x3.
(a) Find dy/dx
(b) What is the slope of the tangent to this curve which passes through the point (1,1)?
(c) Can you confirm this with your graphing calculator?

(3) Consider the curve implicitly defined by the relation x2-xy=2. (a) Find dy/dx using implicit differentiation (b) What is the tangent's slope when (x,y) = (2,1)? (c) Solve for y and find dy/dx and the slope of the tangent through (2,1) directly.


















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