Answer:
Instantaneous slope is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
the instantaneous slope of y=-5\x at x=5
[tex]y=\frac{-5}{x}[/tex]
To find instantaneous slope we take derivative of y
Derivative of 1/x is -1/x^2
[tex]y'=\frac{5}{x^2}[/tex]
We need to find out instantaneous slope at x=5
so we plug in 5 for x in y'
[tex]y'=\frac{5}{x^2}[/tex]
[tex]y'=\frac{5}{5^2}[/tex]
[tex]y'=\frac{5}{25}[/tex]
[tex]y'=\frac{1}{5}[/tex]
Instantaneous slope is [tex]\frac{1}{5}[/tex]
