Question

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

Options

• \[f'(x_0)>0\].

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

• \[f(x_0)=c\] for one value of \[x_0\].

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

Answer 1

Decreasing at \[x_0\] requires an open interval around \[x_0\]. On that interval, the function must be decreasing.