g(t) = k/k + t2 where k is a fixed constant. (a) Sketch the graph of g(t) for k = 3. Show all your working and clearly indicate any asymptotes, intervals on which the function is increasing or decreasing, maxima or minima, intervals of concavity and points of inflection.
g(t) = k/k + t2 where k is a fixed constant.
(a) Sketch the graph of g(t) for k = 3. Show all your working and clearly indicate any asymptotes, intervals on which the function is increasing or decreasing,
(b) The graph of g is symmetric about the y-axis. Find the value of k so that its points of inflection are at t = −10 and t = 10.
(c) Using the value of k you found in (b) alter the formula of g(t) by scaling and shifting to get a new function with maximum point at (60; 400) and points of inflection at t = 50 and t = 70. Call this function h(t), write down its formula and draw a rough
sketch showing the shape of h(t).
(d) Explain in words what the definite integral 60
0 h(t) dt calculates and indicate this on your graph in (c). (You do not need to calculate the integral.)
(e) Your friend looks at the graph of h(t) and says that at t = 65 it is good because there are fewer people who are ill with Covid-19. Do you agree or disagree? Explain.
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