Using the weekly sales function, find the rate at which weekly sales are changing

2,675

Let us define the rate at which weekly sales are changing to be $\frac{dS}{dT}$

Let us define the rate at which weekly advertising costs are changing to be $\frac{dx}{dT}$

Let us define the change in weekly sales with respect to change in advertising costs to be $\frac{dS}{dx}$

$S=1980+45x+.65x^2$

$\frac{dS}{dT}$ = $\frac{dS}{dx}$*$\frac{dx}{dT}$

$\frac{dS}{dT}$ = $(45+1.3x)$*$\frac{dx}{dT}$

Now evaluate $\frac{dS}{dT}$

at x = $8400, $$\frac{dx}{dT}$ = 1250

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Hayley
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Updated on December 06, 2020

Comments

  • Hayley
    Hayley almost 3 years

    Using the weekly sales function $s=1980+45x+0.65x^2$ with $x$ representing weekly advertising costs, find the rate at which the weekly sales are changing when the weekly advertising costs are 8400 dollars and these costs are increasing at a rate of 1250 dollars per week

    • Hayley
      Hayley almost 10 years
      Honestly, Nothing. I don't even comprehend it. :(
    • kaine
      kaine almost 10 years
      You know how to do derivatives?
    • Hayley
      Hayley almost 10 years
      I only know how to do like very simple derivative functions
  • Hayley
    Hayley almost 10 years
    13,706,250? is that right ?
  • kaine
    kaine almost 10 years
    that is the correct value, yes.