Average rate of change question

[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:

Instantaneous:

Find

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

 

[Deleted member 4993]

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:

Instantaneous:

Find

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

Instantaneous rate:

\(\displaystyle \lim_{h\to 0}\dfrac{f(x_1+h)-f(x_1)}{h}\)

\(\displaystyle = \ \lim_{h\to 0}\dfrac{\dfrac{-6}{x_1+h}-\dfrac{-6}{x_1}}{h}\)

\(\displaystyle = \ 6*\lim_{h\to 0}\dfrac{h}{h*(x_1)(x_1+h)}\)

\(\displaystyle = \ \dfrac{6}{{x_1}^2}\)

 

[Scorpy]

I'm sorry about the double post
And I think I did not make my question right. I was asking what would be the tangent line over interval [a,b] (y-b=m(x-a)) if the slope e.g the limit tends to infinity?