Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x> 1

Assuming the function is



For to be differentiable, it necessarily has to be continuous. For this condition to be met, we need





For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have






Now we solve for and :

20000 as first it increases by 2500 then by 5000 so next it will increase by 10000