Question

Find the slope of the curve at the given x-value. Give a decimal answer rounded to three decimal places.

y = x/x^2-1

x = 9

Answer 1

-0.013

Explanation:

You want the slope of the curve y = x/(x² -1) at x = 9.

Derivative

The derivative can be found using the chain rule:

(uv)' = u'v +uv'

Here, we have ...

u = x

v = (x² -1)^-1

Then ...

u' = 1

v' = -1(x² -1)^-2·(2x)

The sum is ...

y' = 1/(x² -1) -2x²/(x² -1)²

Slope

At the point where x = 9, this is ...

y' = 1/(9² -1) -2(9²)/(9² -1)² = 1/80 -162/80² = -82/6400 = -41/3200

y'(9) ≈ -0.013

<95141404393>