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This increase in the size of the budget set implies that the consumer will be better-off as defined with the new consumer optimum at point T. With this increase in income, the consumer chooses to consume both more of both goods indicating that they are both normal goods to that individual.
Consider the function f (x) = (x -1) 2, for. The only critical point is x =1. And the first or second derivative test will imply that x =1 is a local minimum. Looking at the graph (see below) we see that the right endpoint of the interval [0,3] is the global maximum. This leads us to introduce the new concept of endpoint extrema. Indeed, if c is an endpoint of the domain of f (x), then f (x) is said to have an endpoint maximum at c iff for all x in the domain close to c.