I need help with this. Thank you. Please be organized with the answers, and complete the graphs.

1. The graph of f(x) is shown to the right. On the same grid, draw a sketch of f'(x). 2. Choose one of the following to answer: Explain, based on the shape of the graph, why Explain, based on the shape of the graph, why the derivative of any sinusoidal function is also the derivative of any exponential function is also going to be a sinusoidal function. Include a going to be an exponential function. Include a sketch with your response. sketch with your response.4. Determine the 75" derivative of each of the following functions. a f(x) = xe' bj f(x) = 3cos 2x5. The derivatives of three different functions are given below. Determine a possible equation for the original function in each question. a) f(x) = 3x3 +8x +5 f (x) = g'(x)= - 3 b) ( x - 1)' g(x)= h(x)= 3(x+5)(3x -4)-3(x + 5) (3x - 4) h(x) = c) 6. For what value(s) of k, does the function / (x) = Aek , where A is some constant, satisfy the following relationship: f" (x)+ f (x) - 12f(x) =07. In the two questions that follow, the function /(x)=b* is an exponential function. Think carefully about what each graph is showing you. a) The graph of /(x) is shown below. g(x) = f(x) On the same grid, sketch the functions: b) The graph of f(x) is shown below. g (x) = f ( x ) On the same grid, sketch the functions: and f(x) f(x) and f"(x) f(x) g(x)