Use the intermediate value theorem to determine whether the function f(x) = x³ + x-4 has a root or not between x = 1 and x = 2. If yes, then find the root to five decimal places. Does the given function have a root between the interval [1, 2]? If yes, then find the root. Choose the correct answer below. O A. Yes, the given function has a root between [1, 2] and the root is (Type an integer or decimal rounded to five decimal places as needed.) C O B. No, the given function has no root between [1, 2].

b. Tell if the piece-wise function is continuous on the given interval. Put a CHECK MARK AFTER the interval if it is continuous. Put an EX MARKX AFTER the interval if it is discontinuous. [-3, -2] (0, 1) [-4, -3) [-1, 1) (1, 3] (2,4] -1 t Using the graph above, write 1 interval where the function is continuous and 1 interval where it is discontinuous.

Find the largest open intervals on which the function is concave upward or concave downward, and find the location of any points of inflection. 3 f(x) = -a X-3 Select the correct choice below and fill in the answer boxes to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) O A. The function is concave upward on and concave downward on O B. The function is concave upward on There are no intervals on which the function is concave downward. O C. The function is concave downward on There are no intervals on which the function is concave upward.

a. Find the open interval(s) on which the function is increasing and decreasing. b. Identify the function's local and absolute extreme values, if any, saying where they occur. f(x)=x¹/3 (x²-9) a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is increasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function is never increasing. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is decreasing on the open interval(s) (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.) OB. The function…