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Assume that all of the functions are twice differentiable and the second derivatives are never 0.
(a) If f and are positive, increasing, concave upward functions on I, show that the product function fg is concave upward on I.
(b) Show that part (a) remains true if f and are both decreasing.
(c) Suppose f is increasing and is decreasing. Show, by giving three examples, that fg may be concave upward, concave downward, or linear. Why doesn t the argument in parts (a) and (b) work in this case? |
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