Find an equation for the line tangent to the graph of at the point (a, f(a)) for a : 1. "a at) 5:ce The graphs of the function F (leftr in blue) and G (right, in red) are below. F :6 Let P(m) = F(w)G(:c) and Q(:E) = ( ) . Calculate the following derivatives. r (a). P'(6) = C] (b). Q'(1) =8 Note: You can click on the graphs to enlarge the images. COS X Suppose that f ( ) = -5 and f' ( ) = 8, and let g(x) = f(x) sin x and h(a) = f (ac) Answer the following questions. 1. Find g'(7 / 3). Answer: g' (7 / 3) = 2. Find h' (7 / 3). Answer: h' (7/3) =If f (ac) = 5 cos (8 In (a ) , find f'(x). Answer: dy Find for the function y = x 5 cos(a) dx dy dxThe curve with equation 2y3 + y2 y5 = $4 2:33 -l- :32 has been likened to a bouncing wagon (graph it to see why). Find the xcoordinates of the points on this curve that have horizontal tangents. List them below, separating the values with commas. no Suppose f is a onetoone' differentiable function and its inverse function f'1 is also differentiable. One can show, using implicit differentiation (do it!), that _1, _ 1 U "W f'(f'1(w)) Find (fl)'(4) if f(1) = 4 and f'(1): 2/7. (f'1)'(4)=