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10 Apr 2020
Assume that all of the functions are twice differentiable and the second derivatives are never 0.
If f and g are positive, increasing, concave upward functions on I, show that the product function f g is concave upward on I.
(b) Show that part (a) remains true if f and g are both decreasing.
(c) Suppose f is increasing and t is decreasing. Show, by giving three examples, that f g may be concave upward, concave downward, or linear. Why doesn’t the argument in parts (a) and (b) work in this case?
Assume that all of the functions are twice differentiable and the second derivatives are never 0.
If f and g are positive, increasing, concave upward functions on I, show that the product function f g is concave upward on I.
(b) Show that part (a) remains true if f and g are both decreasing.
(c) Suppose f is increasing and t is decreasing. Show, by giving three examples, that f g may be concave upward, concave downward, or linear. Why doesn’t the argument in parts (a) and (b) work in this case?
Beverley SmithLv2
13 May 2020
can either positive or negative on I, depending on values of
on I..