MathDB
Putnam 1970 B2

Source: Putnam 1970

May 17, 2022
Putnamalgebrapolynomial

Problem Statement

The time-varying temperature of a certain body is given by a polynomial in the time of degree at most three. Show that the average temperature of the body between 99 am and 33 pm can always be found by taking the average of the temperatures at two fixed times, which are independent of the polynomial. Also, show that these two times are 10 ⁣: ⁣1610\colon \! 16 am and 1 ⁣: ⁣441\colon \!44 pm to the nearest minute.