College math

Question

A patient has an illness that typically lasts about 24 hours. The temperature, T, in degrees Fahrenheit, of the patient t hours after the illness begins is given by:
T(t)=−0.03t^2+0.696t+98.3

Round all answers to the questions below to 1 decimal place.
When does the patient's temperature reach it maximum value?

 

What is the patient's maximum temperature during the illness?

Answer 1

This is a maximum problem from calculus, although you can do it from knowledge of algebra.

The derivative -.06t + .696 which gives t = 11.6 for the maximum point

 

OR

 

from algebra, we know that the max or min or a parabola occurs at x = -B/A

(where the equation is Ax² + Bx + C

This gives the same answer