If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate .
We have
Expand the numerator using the binomial theorem, then simplify and compute the limit.
In general, the derivative of a power function is
. (This is the aptly-named "power rule" for differentiation.)
Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be , the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
Let equalize the resulting expression to zero and solve afterwards:
Second Derivative Test
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
The maximum sustainable yield is 202500 swordfishes.