MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability
Problem
During a spring day, the air temperature T(t) (in degrees Celsius) is continuously recorded at a weather station, where t is the number of hours after 6:00 a.m. The data show T(0)=12 and T(10)=23.
(a) Explain why there must be a time t1 between 6:00 a.m. and 4:00 p.m. for which T(t1)=20.
(b) Meteorologists claim that the temperature also reached exactly 15∘C at least once during the same period. Identify two specific times t=a and t=b (with 0≤a<b≤10) at which the recorded temperatures guarantee the claim, and justify your reasoning.
(c) Discuss one limitation of using only endpoint temperature data to draw conclusions about intermediate temperatures, and propose an additional measurement that would strengthen the claim in part (b).