(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) On what interval is f(x) = xlnx decreasing?

b) On what interval is f concave upward?

2. Relevant equations

d /dx(lnx) = 1 / x

d /dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x) (Product Rule)

3. The attempt at a solution

a) f'(x) = (x)d/dx(lnx) + (lnx)d/x(x)

= x * 1 / x + lnx

= lnx

According to lnx graph, f(x) decreasing when 0 < x < 1

b) f''(x) = 1 / x

According to 1 / x graph f concave upward when x < 0

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# Homework Help: Decreasing/concave upward: xlnx

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