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Math Help - Rates and Gradient of a Function

  1. #1
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    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

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  2. #2
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    Quote Originally Posted by Snowboarder View Post
    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 \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 k t^n is 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.
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