Find the absolute maximum and absolute minimum of function #14 on the specified interval (if any) of 1/x^2 ;x>0

Question

finding absulute maxiumum and minimum of a problem in busniess caculas

 

Answer 1

To find the min and max, first differentiate the function to see if there are any local min and max:

 

f(x) = 1 / x² = x^-2

f'(x) = -2x^-3 = -2/x³

 

Set the derivative to 0:

 

-2/x³ = 0

 

This equation has no finite solution.  A non-zero number divided by any finite number cannot equal 0.

 

So generally if there is no point at which the derivative is 0, you look at the boundaries of the interval as candidates for min and max.  However, the interval is not closed, so there are no boundary points you can check.  The function grows infinitely as x approaches 0 from above, and it approaches 0 as x approaches infinity.  So in fact, this function does not have a min or max in the interval.