Question

Last question. Please help me finish this last part of an assignment I've been working on all day. A particle moves along the curve y = 3x² + 1 in such a way that the y value is increasing at the rate of 3 units per second. At what rate is x changing when x = 2?

Answer 1

$\bf y=3x^2+1\implies \cfrac{dy}{dt}=\stackrel{chain~rule}{6x\cfrac{dx}{dt}}+0\implies \cfrac{\frac{dy}{dt}}{6x}=\cfrac{dx}{dt} \\\\\\ \begin{cases} \frac{dy}{dt}=3\\\\ x=2 \end{cases}\implies \cfrac{3}{6(2)}=\cfrac{dx}{dt}$