Question

Find the maximum product of two numbers (not necessarily integers) that have a sum of 100. (Use the First Derivative Test.)

Answer 1

We have to use condition to find maximum / minimum

* when f'(x) >0 => function increasing graph y=f(x) is moving upward

* when f'(x) <0 => function decreasing graph of y=f(x) moving downward

* at critical point f '(x) =0 or undefined , function changes from increasing to decreasing or vice versa at critical point   

* If function changes from increasing to decreasing at critical point the that critical point become point of maximum [ f"(x) <0 ]

* If function changes from decreasing to increasing at critical point the that critical point become point of minimum [f "(x) >0 ]

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