The thermic effect of food (TEF) is the increase in metabolic rate after a meal. To model TEF which is measured in kJ/h, researchers use the following functions: S (t) = 175.9teīš g (t) = 113.6te where f (t) is the TEF for a lean person and g (t) is the TEF for an obese person respectively and t, is the time in hours. Find the marimum value of the TEF for both individuals. Solve the above, by answering the following questions: a) Examine both functions above and then rewrite the TEF as a single generalfunction h(t) by replacing the numerical constants in f (t) and g (t) with the symbolic constants a and b. (b) Calculate the derivative h' (t). (c) Find the intervals of increase or decrease of h(t). (d) Using your answerfound in part (c) above, find the maximum TEF fora lean person and the maximum TEF for an obese person respectively by substituting the appropriate values fora and b. (e) Calculate the derivative h" (t). (f) Using your answerfound in part (e) above, find the inflection point for the graph of f (t) (for a lean person) and for the graph of g (t) (for an obese person) respectively and interpret in your own words the physical meaning of this term.|

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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.