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

1 Answer | Add Yours

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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.

We’ve answered 318,988 questions. We can answer yours, too.

Ask a question