Question

What is the instantaneous slope of y=-5\x at x=5

Answer 1

`y=-5x^(-1)`

`(dy)/(dx)=(5)/(x^(2))`
The instantaneous slope at x = 5 is 1/5.

The answer is 1/5.

Answer 2

Instantaneous slope is
`(1)/(5)`

Explanation:

the instantaneous slope of y=-5\x at x=5

`y=(-5)/(x)`

To find instantaneous slope we take derivative of y

Derivative of 1/x is -1/x^2

`y'=(5)/(x^2)`

We need to find out instantaneous slope at x=5

so we plug in 5 for x in y'

`y'=(5)/(x^2)`

`y'=(5)/(5^2)`

`y'=(5)/(25)`

`y'=(1)/(5)`

Instantaneous slope is
`(1)/(5)`