# 2 calculus: local max questions

**Question description**

1.Give an example of a continuous function that is defined for all x > 0 and such that x=1 is a local maximum but not a global maximum.(1.you have to find such a function. 2.explain why the function has the desired properties.)

2.The function f(x)=ln(x) is defined for x > 0. Show that f''(x) <0 and that f(x) has no critical points for x = 1. ( This problem shows why the Global SOC theorem starts by assuming that f(x) has a critical point x*. Here we have a function where f''(x) < 0 and there is no global maximum.)

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