(a) Find the open intervals on which the function shown in the graph is increasing and decreasing. (b) Identify the function's local and absolute extreme values, if any, saying where they occur. -4 -2 -2. (a) On what open intervals is f increasing? Choose the correct answer below. O A. (4,8) and (-2,1) O C. (-8,-2). (1,4), and (-2,1) О в. (-2,1) O D. (-8.-2). (1,4), and (4,8) On what open intervals is f decreasing? Choose the correct answer below. O A. (1,4), and (-2,1) O C. (-8.-2). (1,4), and (4,8) О в. (-21) O D. (4.8) and (-2.1) (b) At which points do the function's absolute maximum and local maximum values occur? Choose the correct answer below. O A. Absolute maximum at (8,6), other local maxima at (-8,-2) and (1,-2) (a) Find the open intervals on which the function shown in the graph is increasing and decreasing (b) Identify the function's local and absolute extreme values, if any, saying where they occur. 6 -4 O B. Absolute maximum at (8,6), other local maxima at (-2,4) and (4,2) O C. No absolute maximum, local maxima at (-2,4) and (1,- 2) O D. No absolute maximum, local maxima at (-8,- 2) and (1, - 2) At which points do the function's absolute minimum and local minimum values occur? Choose the correct answer below. O A. No absolute minimum, local minima at (-2,4) and (4,2) O B. Absolute minimum at (8,6), other local minima at (-8,- 2) and (4,2) OC. No absolute minimum, local mimima at (-8,- 2) and (1,- 2) O D. Absolute minimum at (8,6), other local minima at (-2,4) and (4,2)
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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