Answer:
Step-by-step explanation:
 
        
             
        
        
        
For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that  is such that
 is such that

Obviously, both limits are 0, so  is indeed continuous at
 is indeed continuous at  .
.
Now, for  to be differentiable everywhere, its derivative
 to be differentiable everywhere, its derivative  must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:
 must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:

and at this time, we don't know what's going on at  , so we omit that case. We want
, so we omit that case. We want  to be continuous, so we require that
 to be continuous, so we require that

from which it follows that  .
.
 
        
             
        
        
        
By definition, the power is given by:
 
 By definition, the power is given by:
 Where,
 W: Work done
 t: time
 Clearing the time we have: 

 Substituting values we have: 

 Making the corresponding calculations we have: 
 Answer:
 Answer:
 is needed for a 15,000 W engine to do 1,800,000 J of work about:
  
 
        
        
        
The total number of fish bought was 320. And you know she bought two types of fish. The best way to solve this is guess and check. It would be the fastest. So she bought 7 times as many trigger-fish as parrot fish that means the number of trigger-fish bought was 7p. This means 320 = 7p +p. So all you do is take educated guesses for the number of parrot fish and check if it is right. So if she bought 50 parrot fish. 7(50) + 50 = 400. Close but a bit high. Lets keep guessing. 7(35) + 35 = 245. So now we know the answer is between 50 and 35. So lets try 40. 7(40) + 40 =320. That works so we know she bought 40 parrot fish and 280 trigger-fish.