A thermometer shows at 8:00 a.m

MATHEMATICS · Subjective · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A thermometer shows

15^{\circ}\text{C}

at 8:00 a.m. and

23^{\circ}\text{C}

at noon. The temperature

T(t)

, measured in degrees Celsius, is known to be differentiable for

8\le t\le12

, where

t

is time in hours after midnight. Explain in one or two sentences why there must be a time between 8:00 a.m. and noon when

T(t)=20^{\circ}\text{C}