Question

How do you find the instantaneous slope of `y=1/x` at x=4?

Answer 1

`-1/16`

Explanation:

The instantaneous slope is determined by differentiating `y` at `x=4`

Differentiating `y` is computed by applying the quotient rule
`color(blue)((u/v)'=(u'v-v'u)/v^2`

`y=1/x`

`y'=color(blue)((1'xxx-x'xx1)/x^2)`

`y'=0-1/x^2`

`y'=-1/x^2`
`y'_((x=4))=-1/4^2=-1/16`

Therefore, the slope of y at `x=4` is `-1/16`