Given that h(x) = f(g(x)), use the graphs of f and g to find h'(5). Show...

  

Transcribed Image Text:

Given that h(x) = f(g(x)), use the graphs of f and g to find h'(5). Show all your work. YA 7 5 3 1 0 I 3 (a) Calculate h(2) and h' (2). (b) Determine an equation of the line tangent to the graph of h at (2, h(2)). 5 y = g(x) 7 X 3. Assume f and g are differentiable on their domains with h(x) = g(f(x)). Suppose the equation of the line tangent to the graph if f at the point (2,-1) is y=2x-5 and the equation of the line tangent to the graph of g at (-1,5) is y=-3x + 2. 4. For the curve 3 + 7y = 10y, complete the following steps. (a) Determine the points where the curve has a vertical tangent line. (Find either z or y-values.) (b) Determine the points where the curve has a horizontal tangent line. (Find both and y-values.) 5. Calculate the derivative of the following function. f(x) = logs (log5 ) 2- (1, 1) Given that h(x) = f(g(x)), use the graphs of f and g to find h'(5). Show all your work. YA 7 5 3 1 0 I 3 (a) Calculate h(2) and h' (2). (b) Determine an equation of the line tangent to the graph of h at (2, h(2)). 5 y = g(x) 7 X 3. Assume f and g are differentiable on their domains with h(x) = g(f(x)). Suppose the equation of the line tangent to the graph if f at the point (2,-1) is y=2x-5 and the equation of the line tangent to the graph of g at (-1,5) is y=-3x + 2. 4. For the curve 3 + 7y = 10y, complete the following steps. (a) Determine the points where the curve has a vertical tangent line. (Find either z or y-values.) (b) Determine the points where the curve has a horizontal tangent line. (Find both and y-values.) 5. Calculate the derivative of the following function. f(x) = logs (log5 ) 2- (1, 1)