Average / Instantaneous rate of change help!

[Calculushelp65]

Hey first time member here looking to see if I could get a little assistance, thanks.

What is the average rate of change of f(x) given f(x) = -6/x from [1,2] and [1,4]


and

What is the instantaneous rate of change of f(x) when x=1

 

[galactus]

The average rate of change is the slope of the secant line from [a,b]

Whereas, the instantaneous rate of change is the slope at said point.


Average:

\(\displaystyle \frac{f(2)-f(1)}{2-1}\)

Instantaneous:

\(\displaystyle \displaystyle \lim_{x_{1}\to 1}\frac{f(x_{1})-f(1)}{x_{1}-1}\)

Find \(\displaystyle f(1)=\frac{-6}{1}=-6\)

\(\displaystyle f(x_{1})=\frac{-6}{x_{1}}\)

\(\displaystyle \displaystyle \lim_{x_{1}\to 1}\frac{\frac{-6}{x_{1}}-(-6)}{x_{1}-1}\)

 

[Calculushelp65]

Thank you so much

 

[Scorpy]

The average rate of change is the slope of the secant line from [a,b]

Whereas, the instantaneous rate of change is the slope at said point.


Average:

\(\displaystyle \frac{f(2)-f(1)}{2-1}\)

Instantaneous:

\(\displaystyle \displaystyle \lim_{x_{1}\to 1}\frac{f(x_{1})-f(1)}{x_{1}-1}\)

Find \(\displaystyle f(1)=\frac{-6}{1}=-6\)

\(\displaystyle f(x_{1})=\frac{-6}{x_{1}}\)

\(\displaystyle \displaystyle \lim_{x_{1}\to 1}\frac{\frac{-6}{x_{1}}-(-6)}{x_{1}-1}\)

Hello,

I just wanted to ask if you want to find the average rate of change over some interval, and what if the slope tends to infinity? What next?

Thanks