Answer:
[tex]\frac{dx}{dt}=-\frac{33}{28} =-1.1786[/tex]
Step-by-step explanation:
Given that the price p, in dollars, and number of sales, x, of a certain item follow the equation:
5p+4x+2px=60.
Taking partial derivatives
[tex]5\frac{dp}{dt} +4\frac{dx}{dt}+2x\frac{dp}{dt}+2p\frac{dx}{dt}=0\\(4+2p)\frac{dx}{dt}=(-5-2x)\frac{dp}{dt}\\\frac{dx}{dt}=\frac{-5-2x}{4+2p} \cdot \frac{dp}{dt}[/tex]
When x=3, p=5, dp/dt=1.5
[tex]\frac{dx}{dt}=\frac{-5-2(3)}{4+2(5)} \cdot 1.5\\=\frac{-5-6}{4+10} \cdot 1.5\\=\frac{-11}{14} \cdot 1.5\\\frac{dx}{dt}=-\frac{33}{28} =-1.1786[/tex]
Therefore, x is decreasing at a rate of -1.1786.
