How can I find the instantaneous rate of change? The function is: x^2-6x-5

Question

whpalmer4 · Answer

The instantaneous rate of change will be the value of the derivative at the point where you wish to find the instantaneous rate of change.

whpalmer4 · Answer

So, find the derivative (with respect to $x$) of the function, then evaluate the derivative at the value of $x$ where you wish to find the rate of change.

jsmit200 · Answer

They tell me to compare this rate of change with the instantaneous rates of change at the endpoints of the interval.

jsmit200 · Answer

The interval I have is [-1,3]

whpalmer4 · Answer

so are you to find the average rate of change over the interval?  The problem as you have provided it is a bit sketchy...

jsmit200 · Answer

Let me provide a snap shot. Give me one moment.

whpalmer4 · Answer

The average rate of change of a function $f(x)$ over the interval $[a,b]$ is 
$$\frac{f(b)-f(a)}{b-a}$$

jsmit200 · Answer

attachment

phi · Answer

the derivative of your parabola is 2x - 6
evaluate that at each of your endpoints.

phi · Answer

if you look closely at your question, they are asking about
f'(-1)  and f'(3)
f' means  df/dx