The Relationship Between the Rate of a Certain Chemical Reaction $R ( T ) = 0.1 \left( - 0.05 T ^ { 3 } + 4 T ^ { 2 } + 120 \right)$

Essay

The relationship between the rate of a certain chemical reaction and temperature under certain circumstances is given by $R ( T ) = 0.1 \left( - 0.05 T ^ { 3 } + 4 T ^ { 2 } + 120 \right)$ grams/sec, where R is the rate of reaction and T is the temperature (in žC).
(a) Find the temperature T at which the reaction rate reaches its maximum.
(b) What is the maximum reaction rate?