2. Consider the function f(x) = -2x2 = xe (a) Determine the y-intercept and the x-intercept(s), if there are any. (b) Determine all critical points of f. (Identify both the r and y values of the critical points.) (c) Construct a sign chart for f' (x) and use it to classify the critical points as local maxima, local minima, or neither of those. (d) Construct a sign chart for f"(x) and use it to determine the points of inflection of f. (Identify both the r and y values of the points of inflection.) (e) Sketch the graph of y = f(x).
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.
Answer all parts (a, b, c, d, e) from the following problem:
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