Question

Which statement expresses the Extreme Value Theorem?

Options

• A function with \[f'(x)=0\] has no absolute extrema.

• A continuous function on a closed interval \[a,b\] will attain its absolute maximum and absolute minimum value at least once in that interval.

• A differentiable function on an open interval will attain its absolute maximum and absolute minimum value at least once.

• A continuous function has absolute extrema only at interior points.

Answer 1

The Extreme Value Theorem requires a continuous function and a closed interval \[a,b\]. Under these conditions, both absolute extrema are attained at least once.