Answer: The quantity demanded is decreasing at the rate of [tex]\dfrac{1}{6}\ thousands/week[/tex]
Step-by-step explanation:
Since we have given that
[tex]p+x^2=225[/tex]
Here, p is the price and x is the quantity demanded.
Price per tire is increasing at the rate of $2/week.
So, [tex]\dfrac{dp}{dw}=2[/tex]
Differentiating the given equation w.r.t 'w', so we get that
[tex]\dfrac{dp}{dw}+2x\dfrac{dx}{dw}=0\\\\2+2\times 6\dfrac{dx}{dw}=0\\\\2+12\dfrac{dx}{dw}=0\\\\\dfrac{dx}{dw}=\dfrac{-2}{12}=-\dfrac{1}{6}[/tex]
Hence, the quantity demanded is decreasing at the rate of [tex]\dfrac{1}{6}\ thousand/week[/tex]
