For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. h(x) = 4x - 48x a) What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box(es) complete your choice. O A. The relative minimum point(s) is/are and the relative maximum point(s) is/are. (Simplify your answers. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O B. The relative maximum point(s) is/are and there are no relative minimum point(s). (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O C. The relative minimum point(s) is/are and there are no relative maximum point(s). (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points.

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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.