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, 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, maxima or minima, intervals of concavity and points of inflection.
(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. (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.
Definition Definition Highest point, either on the entire domain or on the given range of a function. The plural form of 'maximum' is 'maxima'.
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