Suppose the following data points are generated by a smooth function f(x): 1/3 2/3 4/3 5/3 2. f(x) 1.8415 1.9954 1.7231 1.1411 0.4987 0.0710 0.0411 The approximation of f(x) dx using the trapezoidal rule with 3 sub-intervals is:

Use the first derivative test to find the location of all local extrema in the interval (0, 10) for the function given below. f(x) = 5x² In (4x) If there is more than one local maxima or local minima, write each value of x separated by a comma. If a local maxima or local minima does not occur on the function, enter Ø in the appropriate box. Enter exact answers. Provide your answer below: The local maxima occur at x = The local minima occur at x = [].

For the following function, f(x) = a* – 12a", determine the following (enter DNE if it does not exist): a. Intervals where f is increasing or decreasing (in interval notation): Increasing: Preview Decreasing: Preview b. Local minima or maxima of f (enter as a list, separated by commas): Local minima at a = Preview Local maxima at æ Preview c. Intervals where f is concave up and concave down (in interval notation): Concave up: Preview Concave down: Preview d. The inflection point(s) of f (enter as a list, separated by commas): Inflection point(s) at æ = Preview Get Help:

For the following functions. Please show all evidence. (a) Identify all local extrema, (max or min.) (I want to see evidence of the first derivative test) (b) Find the open intervals on which it is increasing and decreasing. (c) Describe the concavity of the graph. (I want to see evidence of the second derivative test) (d) Do any algebra work that is helpful: find all intercepts, find all discontinuities, discuss end behavior Then use this information to sketch the graph. 2) f(x) = +x 3) f(x) = (x – 1)°(2x – 1) 1) f(x) = 3x* -4x