# Continuous function/Between two local maxima/Minimum/Exercise

Let

be a continuous function defined over a real interval. The function has at points , , local maxima. Prove that the function has between and

has at least one local minimum.Let

- $f\colon I\longrightarrow \mathbb {R}$

be a continuous function defined over a real interval. The function has at points ${}x_{1},x_{2}\in I$, ${}x_{1}<x_{2}$, local maxima. Prove that the function has between ${}x_{1}$ and ${}x_{2}$

has at least one local minimum.