20 1 Suppose F X X 2 Cos X For X In 0 2 5 A Find All Critical Numbers Of F And Determine The Intervals Where 1 (37.5 KiB) Viewed 54 times
20 1 Suppose F X X 2 Cos X For X In 0 2 5 A Find All Critical Numbers Of F And Determine The Intervals Where 2 (31.87 KiB) Viewed 54 times
[20] 1) Suppose f(x)=x+2 cos(x) for x in [0, 2]. [5] a) Find all critical numbers of f and determine the intervals where f is increasing and the intervals where f is decreasing using sign analysis of f'. f'(x)=. Critical Numbers of f in [0, 2m]: Sign Analysis of f' (Number Line): Intervals where f is increasing: Intervals where f is decreasing: [2] b) Find all points where f has local extrema on [0,27] and use the First Derivative Test (from Section 3.3) to classify each local extrema as a local maximum or local minimum. Local Maxima (Points):_ Local Minima (Points): [2] c) Using the Closed Interval Method (from Section 3.1), find all points where f has absolute maximum and minimum values on (0,27]. Absolute Maxima (Points): Absolute Minima (Points):
[6] d) Using the partition numbers and sign analysis of f", find the intervals where f is concave upward and where f is concave downward. Find the inflection points of f. f"(x) Partition Numbers of f" in [0, 2m]: Sign Analysis for f" (Number Line): Intervals where f is concave upward: Intervals where f is concave downward: Inflection Points of f: [5] e) Sketch the graph of y = f(x). Label the axes and indicate the scale on the axes. Label each local extrema (use "max" or "min") and inflection point (use "IP"). Suggestions: For the r-scale, divide [0, 27] into 12 subintervals of equal length of /6. Determine the y-scale based on the absolute maximum and minimum of f found in part (c).
Join a community of subject matter experts. Register for FREE to view solutions, replies, and use search function. Request answer by replying!