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Answer each of the following questions 'yes' or 'no', and justify your answer.
(a) Suppose f(x) is an increasing function of one variable. Is f(x) quasiconcave?
(b) Suppose f(x) is a decreasing function of one variable. Is f(x)quasiconcave?
(c) Suppose f(x) is a function of one variable and there is a real number b such that f(x) is decreasing on the interval (-∞,b] and increasing on [b,+∞). Is f(x) quasiconcave?
(d) Suppose f(x) is a function of one variable and there is a real number b such that f(x) is increasing on the interval (-∞,b] and decreasing on [b,+∞). Is f(x) quasiconcave?
(e) You should now be able to come up with a characterisation of quasiconcave functions of one variable involving the words 'increasing' and 'decreasing'.
Consider the examples from children's speech below. Using the linguistic terminology you have learned,explain what mistakes the children make.
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