Question

Let \[x_0\] be in the domain of a real-valued function \[f\]. When is \[f\] increasing at \[x_0\]?

Options

• \[f'(x_0)<0\].

• There exists an open interval containing \[x_0\] in which \[f\] is increasing.

• \[f(x_0)=0\].

• There exists an open interval containing \[x_0\] in which \[f\] is constant.

Answer 1

Increasing at \[x_0\] is a local condition. There must be an open interval containing \[x_0\] on which the function is increasing.