Question

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

Answer 1

$y=-5x^{-1}$
$\frac{dy}{dx}=\frac{5}{x^{2}}$
The instantaneous slope at x = 5 is 1/5.

The answer is 1/5.

Answer 2

Answer:

Instantaneous slope  is $\frac{1}{5}$

Step-by-step explanation:

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

$y=\frac{-5}{x}$

To find instantaneous slope we take derivative of y

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

$y'=\frac{5}{x^2}$

We need to find out instantaneous slope at x=5

so we plug in 5 for x in y'

$y'=\frac{5}{x^2}$

$y'=\frac{5}{5^2}$

$y'=\frac{5}{25}$

$y'=\frac{1}{5}$

Instantaneous slope  is $\frac{1}{5}$