It will reach a max when R '(T) = 0
R'(T) = .1(-.15T^2 + 8T) = 0
.15t^2 - 8t = 0
t(.15t - 8) = 0
t = 0 , (at the beginning)
or
t = 8/.15 sec = 160/3 sec
find R(160/3) to get that maximum
The relationship between the rate of a certain chemical reaction and temperature under certain circumstances is given byR(T)=0.1(−0.05T^3+4T^2+120)grams/sec, where Ris the rate of reaction and Tis the temperature (in °C).
a)Find thetemperature T at which the reaction rate reaches its maximum?
b)What is the maximum reaction rate?
1 answer