Hi there I'm not able to reproduce the answer for the value of C=4 in part (v) by maximising the equation 4x/(500+x)=0 Could someone please step me through this?
Probably a bit late for an answer - but differentiation shows there's no turning point. So we just look at the boundaries x>0. When x=0 we have 0 and as x tends to infinity the graph tends to 4. So 4 is the maximum.
Without drawing the graph could you deduce this because the infinity would be multiplicative in the numerator but only additive in the denominator...therfore the solution as x tends to infinity will be the numerator? Thanks!
Compared to infinity on the denominator the 500 becomes insignificant. Hence it tends to 4x/x = 4. But easiest way is to use a large number in your calculator and see what happens, eg putting in 1,000,000 gives 3.998.
