How to calculate the average rate of change for a function?

Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.

Question

How to calculate the average rate of change for a function?


Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.

agent0smith · Answer

Use the slope formula, m=(y2-y1)/(x2-x1)

your x1 is 0, so plug it into the function to find y1

x2 is 1, so plug it into the function to find y2

agent0smith · Answer

Avg. rate of change is the same as that, using the slope formula.

anonymous · Answer

So, the answer is 0?

agent0smith · Answer

Idk i didn't work it out yet. If you worked out y2 and y1 correctly, and used the slope formula.

anonymous · Answer

Okay. I got zero. Can you help me with another problem, please?

agent0smith · Answer

From looking at a graph, no, the avg rate of change is not zero

agent0smith · Answer

Recalculate y2 and y1. Show your work.

anonymous · Answer

This is what my graph showed me.

agent0smith · Answer

That clearly shows the avg rate of change is not 0

your x1 is 0, so plug it into the function to find y1... −x4 + 4x3 − 2x2 + x + 1 is your function

x2 is 1, so plug it into the function to find y2

agent0smith · Answer

then avg rate of change =(y2-y1)/(x2-x1)

anonymous · Answer

Is y2 3?

agent0smith · Answer

probably

agent0smith · Answer

Or 4. idk, just plug x=1 and evaluate...

undeadknight26 · Answer

ansa is 2 for future students.