# Rates and Gradient of a Function

• May 10th 2008, 03:19 PM
Snowboarder
Rates and Gradient of a Function
During a 31 day (month) long Australasian advertising campaign the total sales of a particular magazine is given by the formula S(t)= 4t^2 +80t +12000.

a) Find the average of change in sales S
(i) from t=6 to t=13 days
(ii) from t=26 to t = 31 days

(b)Use differentiation to find the instantaneous rate of change of sales when t = 26 days.
(c) Interpret the result from (a) (ii) and (b) with respect sales expectation

• May 10th 2008, 03:34 PM
mr fantastic
Quote:

Originally Posted by Snowboarder
During a 31 day (month) long Australasian advertising campaign the total sales of a particular magazine is given by the formula S(t)= 4t^2 +80t +12000.

a) Find the average of change in sales S
(i) from t=6 to t=13 days
(ii) from t=26 to t = 31 days

(b)Use differentiation to find the instantaneous rate of change of sales when t = 26 days.
(c) Interpret the result from (a) (ii) and (b) with respect sales expectation

Formulae you should know and be able to use:

Average rate of change of f(t) between t = a and t = b is given by $\displaystyle \frac{f(b) - f(a)}{b - a}$.

The instantaneous rate of change of a function is given by the derivative of the function.

The derivative of $\displaystyle k t^n$ is $\displaystyle n k t^{n-1}$.

The derivative of a sum (or difference) of functions is equal to the sum (or diference) of the derivative of each function.