Question

A particle moves along the curve f(x). As it reaches the point (3; 2), the y-coordinate is increasing by 1.2 cm/sec. At what rate is the x-coordinate changing at that instant?

Answer 1

y=\[\sqrt[3]{x^{2}-1}\]

Answer 2

here they actually give you the formula

Answer 3

I take the derivative.

Answer 4

but then what?

Answer 5

yes, don't forget that \(x\) is a function of \(t\) also, your answer should have a \(x'\) in it

Answer 6

oh, so I just plug in 1.2 to x' and 3 into x and get y'?

Answer 7

at the end, yes
you should get as a first step
\[y'=\frac{2xx'}{3\sqrt{x^2-1}^2}\]

Answer 8

I got 0.6