Question: Consider the function f(x) = (ab x + (1 - a)c x ) 1/x , where a, b, and c are positive real numbers with

Consider the function f(x) = (abx + (1 - a)cx)1/x, where a, b, and c are positive real numbers with 0

a. Graph f for several sets of (a, b, c). Verify that in all cases f is an increasing function with a single inflection point, for all x.

b. Use analytical methods to determinelim f(x) х—0' in terms of a, b, and c.

c. Show that lim f(x) max {b, c} = and lim f(x) 0' lim f(x) max {b, c} =for any 0

d. Estimate the location of the inflection point of f.

lim f(x) 0' lim f(x) max {b, c} =

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