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

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neela | High School Teacher | (Level 3) Valedictorian

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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.