### Math Notes

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#### Differential Calculus Solutions

##### Topics || Problems

The number of newspaper copies distributed is given by C = 50 t2 - 200t +10 000, where t is in years. What is the minimum number of copies distributed from 1995 to 2002?

Solution:

$$\frac{dC}{dt} = 100t - 200$$

$$\frac{d^2C}{dt^2} = 100 > 0$$ thus Minimum

$$0 = 100t - 200$$

$$t = 2$$

$$C = 50(2)^2 -200(2) +10 000$$

$$C = 9800$$