Answer:
a
     f'(t) is  negative
b
  The  unit is degC/min
c
 At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.          
Step-by-step explanation:
From the question we are told we are told that  
    The  equation for the temperature of a cup of coffee place on a counter is 
          
Here  t is the time in minutes the  coffee was put on the counter
 Generally  f(t)'  is the derivative of  f(t) at it represents the change of the temperature of the cup of coffee with respect to time 
  Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence  f(t)' is  negative 
 Generally the unit of the temperature is in degrees Celsius while that of time is  in minutes 
   So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e  degC/min)
   From the question we are told that 
         
i.e  the rate of change of temperature after 35 minutes is  1.5 
and 
          
i.e the temperature of the cup of coffee after 35 minutes is  67 degC
 Now after another   t=  30  seconds =   the  rate  of change of the temperature of the cup of  coffee is
 the  rate  of change of the temperature of the cup of  coffee is  
            
 
=>         
 
=>         
     
So
 At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.