Homework t(4)

question 2

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the inflection points. f(x) = -x0 + 24x5 -24x +2 For what interval(s) of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) O B. The graph is never concave upward. For what interval(s) of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. (Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.) O B. The graph is never concave downward. Determine the x coordinates of any inflection points of the graph of f(x). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. X= (Type an exact answer. Use a comma to separate answers as needed.) O B. There are no inflection points.Find the intervals on which f(x) is increasing and the intervals on which f(x) is decreasing. Then sketch the graph. Add horizontal tangent lines. f(x) = x4 - 8x2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on (Type your answer using interval notation. Use a comma to separate answers as needed.) O B. There is no solution. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is decreasing on (Type your answer using interval notation. Use a comma to separate answers as needed.) O B. There is no solution. Choose the correct graph of f(x) = x# - 8x with the correct horizontal tangent line below. O A. O B. O C. O D. 192.32Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. f(x) = X5 + 4x -21 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is increasing on. (Type your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.) O B. The function is never increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The function is decreasing on. (Type your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.) O B. The function is never decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Type integers or simplified fractions. Use a comma to separate answers as needed.) O A. The function has local maxima f(c) = and local minima f(c) =. O B. The function has local minima f(c) = , and no local maxima. O C. The function has local maxima f(c) = , and no local minima. O D. The function has no local extrema.Afence is to he built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of material that costs $4 per foot. The material for the fourth side costs $12 per foot. Find the dimensions of the rectangle that will allow for the most economical fence to be built. The short side is ft and the long side is ft. A T-shirl manufacturer is planning to expand its workforce. lI estimates that the number of Tshirts produced by hiring x new workers is given by T(x) = - [3.75x4 +12x3, O st 12. When is the rate of change of T-shirt production increasing and when is itdecreasing? What is the point of diminishing returns and the maximum rate of change for Tshirt production? Graph Tand T' on Ihe same coordinate system. The rate of d1ange oi T-shirt production is increasing on (Type your answer in interval notation.) The rate of change of T-shirt production is decreasing on (Type your answer in interval notation.) The point of diminishing returns is x = workers. The maximum rate of change for Tshirt production is T-shirts per worker. Graph T and T' on the same coordinate system. 0 A. O B. O c. O D. 5184 y Q a 753 763 m 334 m XE x13- 755 XE,- XE