Suppose y = L(x) = ax+b (with a 0) is the equation of the line tangent to the graph of a one-to-one function f at (xo.Yo). Also, suppose that y = M(x) = cx + d is the equation of the line tangent to the graph of f' at (yo.Xo) . Complete parts (a) through (c) below. ..... a. Express b in terms of a, Xo, and yo. Choose the correct answer below. Yo O B. b=Xo + a O A. b=yo+ a O D. b=yo-axo O C. b=x0 + ayo OF. b=Yo- a E. b=Yo +axo O H. b=X0 - ayo Yo O G. b=X0 a

For each given functions, find the slope of the tangent at a given point using first principle definition. a. y=x^(3)+8  (-2,0) b.y=2x^(2)-(5)/(x+2)  (0,-5/2) c. y=\sqrt(x)  at x=9

The graphs of f and g are shown. Let h(x) = f(g(x)) and s(x) = g(f(x)). y 15 10 5 -2 4 6. 10 (a) Write an equation for h'(x) in terms of f(x), g(x), f'(x), and g'(x). O h'(x) = g'(f'(x))f'(x) O h'(x) = g'(f(x))f'(x) h'(x) = f'(g'(x))g'(x) h'(x) = f'(g(x))gʻ(x) O h'(x) = f'(g'(x))g(x) O h'(x) = g'(f'(x))f(x) Find h'(3). (If an answer does not exist, enter DNE.) (b) Write an equation for s'(x) in terms of f(x), g(x), f'(x), and g'(x). O s'(x) = f'(g(x))g'(x) O s'(x) = g'(f'(x))F'(x) O s'(x) = f'(g'(x))g'(x) s'(x) = g'(f(x))f'(x) s'(x) = f'(g'(x))g(x) s'(x) = g'(f'(x)){x) Find s'(7). (If an answer does not exist, enter DNE.)

Letf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ'(−6) = −4, g(−6) = −4, g′(−6) = −3. Using the above information, compute h' (-6) where h(x) = (f(x))² g(x). h'(- 6) = Number