C(m)=300+5m The rate of change of C(m) is 5. explain what this means in the given context.

C(m) = 300+5m.

We can give a
practical meaning to this.

In a  (large)tank , initially
there is 300 litre of water. A water pipe imputs 5 liter of water every minute. So the
amount collected water C(m) , after m minute  is given by the  equation
:

C(m) = 300 + 5m.

The rate
amount of water increase per minute is obviously 5.

By
calculus,  C(m) = 300+5m.

Differentiating with respect to
the variable m, we get:

C'(m) =
{300+5m}'.

C'(m) = (300)'
+(5m)'.

C'(m) = 0 +5.

C'(m) =
5.

Thus the differential coefficient of C(m), or C'(m)
indicates the rate of change with respect to m is equal to 5 in the given
case. 

The terms,  'rate of change' and 'derivatives' are
very much interrelated. So the term derivative gives lot of additional and related
knowledge.