Consider the function f(x) = 1. Find the first derivative of f(x) with respect to x. 2. Determine the critical points of f (x) (i.e., where the derivative is zero or undefined). 3. Classify the critical points as local maxima, local minima, or points of inflection.

← Perform a first derivative test on the function f(x) = 5x²-3x+4; [-4,4]. a. Locate the critical points of the given function. b. Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). a. Locate the critical points of the given function. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The critical point(s) is/are at x = (Simplify your answer. Use a comma to separate answers as needed.) OB. The function does not have a critical point. b. Locate the minimum value. Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. There is a local minimum at x = your answer.) B. There is no local minimum. Locate the maximum value. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. There is a local maximum at x = (Simplify your…

We have learned how to use derivatives to analyze functions. We have discussed increasing and decreasing regions of functions as well as concavity. We have also discussed how to use this information to determine relative minima and maxima. Let's consider the following function: f (z) = 1. Where is the function increasing and decreasing? 2. What are the critical values of the function? 3. What are the coordinates of the relative minima and maxima of the function?

Please answer parts C, D and E. Show all work.