At a production level of x items, a company finds that the demand is p = 100/sqrt x and the cost is C(x) = x + 1000. What value of x will maximize profit?

word problem

when a certain guitar string is plucked, it vibrates with a frequency  F(t) = 200 sqr( t ) where t  is measured in pounds and F is measured in vibrations per second. find the rate of change  of F with respect to t  when t= 1