Subject: Physical Quemistry

MY QUESTION: In excercise (a) there is an identity: [A]o=e^(-k1t) and [B]= ((k1[A]o)/(k2-k1))(e^(-k1t)-e^(-k2t)) which the professor took

d[B]/dt=0=d/dt[ k1[A]o)/(k2-k1)(e^(-k1tmax)-e^(-k2tmax)

I dont understand how the professor made the process to get from that to the equation

tmax=((1)/(k1-k2))ln(k1/k2)

If someone could enlighten me by providing me with both parts of the same excercise I will apreciate because I dont know how to proceed to do the graph in part (b)

A consecutive reaction is first order has values of velocity constant k1=0.75min-1 and k2=0.25min-1 at certain temperature. If [A]o= 1mol/dm3 , [B]o= 0 and [C]o= 0 a. at what time a B will achieve certain temperature? ANSWER: [B]max= 0.57M , [A] = 0.192M, [C]= 0.24M b. do the graph for [A], [B] and [C] vs t