1 (a) The curve y = 1/(1 + x2) Is called a witch of Maria Agnesl. Find an equation of the tangent line to this curve at the point ( -1, =). y = (b) Illustrate part (a) by graphing the curve and tangent line un the same screen. 2.0 2.0 1.5 0.5 -0.5 -0.5 1.0 O 1.0 2.0 0.5 0.5 -2 -2 2 0.5 0.5 -1.0 -1.0 2 Suppose that f(5) = 3, f '(5) = 6, g(5) = -8, and g'(5) = 2. Find the following values. (a) (fg) ' (5) (b ) (f/g) '(5) (c ) (gin) ' ( 5 ) 3 Tutorial Exercise If f(x) = e*g(x), where g(0) = 2 and g'(0) = 3, find f '(0). Part 1 of 3 We begin by finding the derivative of f(x) = e*g(x). Since this is a product, we use the Product Rule, which states [(x)g(x)] = f '(x)g(x) + f(x)g'(x). Therefore, f ' ( x ) = ex . 9 ( x ) + ex ex ' 9' ( x ) . Part 2 of 3 We need to find f '(0). Recalling that e = , we have the following. F' ( 0 ) = e - g ( 0 ) + e -g' (0 ) = g(0) + g'(0)