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) = 175.9te 9 (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 general function h (t) by replacing the numerical constants in s (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 answer found in part (c) above, find the maximum TEF for a lean person and the maximum TEF for an obese person respectively by substituting the appropriate values for a and b. (e) Calculate the derivative h" (t). (f) Using your answer found 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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Please assist with a, b, c and d

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) = 175.9te
9 (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 general function 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 answer found in part (c) above, find the maximum TEF for a lean person and the
maximum TEF for an obese person respectively by substituting the appropriate values for a and
b.
(e) Calculate the derivative h" (t).
(f) Using your answer found 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.
Transcribed Image Text: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) = 175.9te 9 (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 general function 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 answer found in part (c) above, find the maximum TEF for a lean person and the maximum TEF for an obese person respectively by substituting the appropriate values for a and b. (e) Calculate the derivative h" (t). (f) Using your answer found 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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