GroupHomework #2

It is possible to define a function of the form NiMvLUkiTEc2IjYjSSJ0R0YmLCZJIkFHRiYiIiIqJkkiQkdGJkYrLUkkY29zR0YmNiMsJiomSSJDR0YmRitGKEYrRitJIkRHRiZGK0YrRis= which gives the number of hours of daylight t days after January 1st. a) How long is the period of this function? Use this to determine the value of C.b) What is the longest day of the year? Use this to determine the value of D.c) How many hours of daylight are there on the autumnal equinox? Use this to determine the value of A.d) How many hours of daylight were there today? Use this to determine the value of Be) Use your equation to predict how many hours of daylight there will be on Halloween.

a) Suppose that f'(x) = 1 for all x. Find an algebraic expression for f(x) if NiMvLUkiZkc2IjYjIiIhIiIj.b) Suppose that f'(x) = 1 for all x. Find an algebraic expression for f(x) if NiMvLUkiZkc2IjYjIiIjIiIi.c) Suppose that f'(x) = 5 for all x. Find an algebraic expression for f(x) if NiMvLUkiZkc2IjYjIiIiLCQiIiQhIiI=.d) Suppose that f'(x) = -2 for all x. Find an algebraic expression for f(x) if NiMvLUkiZkc2IjYjIiIlLCQiIiYhIiI=.e) Suppose that f'(x) = m for all x. Find an algebraic expression for f(x) if NiMvLUkiZkc2IjYjSSJhR0YmSSJiR0Ym.

Suppose that a cup of hot coffee is poured into a mug in a room with ambient temperature of 25 degrees Celsius. Let T(t) be the temperature (in degrees Celsius) of the coffee in the cup t minutes after the coffee was poured. a) Describe the graph of T(t).b) What are the units of T'(t)? c) Is T(5) > 0? Justify your answer.d) Is T'(5) > 0? Justify your answer. e) What is the approximate value of T(300)? Explain why.f) What is the approximate value of T'(300)? Explain why.

If the following is a graph of f '(x), answer the questions 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a) Where is f(x) increasing? Where is it decreasing?b) Where is f(x) concave up? Where is it concave down?c) Does f(x) have any local maxima or minima? If so, identify them all.d) Does f(x) have any inflection points? If so, identify them all.e) Rank the following values in increasing order: f(-1), f(0), f(1) and f(3).