I just want to make sure that I understand average rate of change correctly.

[mason.smith97]

The average rate of change is a simple concept. However, I just want to make sure that I understand how to solve a problem. The formula for the average rate of change is [f(x+h) – f(x)] ÷ h, correct? And you can use the coordinates P(x, f(x)) and Q(x+h, f(x+h)), correct? If the two previous statements are correct, then I will work out a problem, and I would like for you to tell me if I am correct.

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F(x)=4x-3 ; x=2

Step 1: I plug the x and the f(x) into coordinates P and Q.

Step 2: After plugging x and the f(x) into coordinates P and Q, I get P(2, 5) and Q(2+h, 18+4h).

Step 3: I then fill in the formula for the avg. rate of change to find the answer. [(18+4h) - 5] ÷ h.

Step 4: After simplifying, I get (13+4h) ÷ h.

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Do I have a correct understanding of how to use the avg. rate of change formula and the coordinates P and Q? The reason that I am asking is because I explained this to my friend, and I just want to be sure that I explained it correctly. We're learning limits, and this equation was used.

To whomever answers this, thank you for taking the time to read this and to respond.

P.S. If there is one or two errors, please excuse me. It is late, and I really needed to post this before I forgot.

 

[Deleted member 4993]

The average rate of change is a simple concept. However, I just want to make sure that I understand how to solve a problem. The formula for the average rate of change is [f(x+h) – f(x)] ÷ h, correct? And you can use the coordinates P(x, f(x)) and Q(x+h, f(x+h)), correct? If the two previous statements are correct, then I will work out a problem, and I would like for you to tell me if I am correct.

---

F(x)=4x-3 ; x=2

Step 1: I plug the x and the f(x) into coordinates P and Q.

Step 2: After plugging x and the f(x) into coordinates P and Q, I get P(2, 5) and Q(2+h, 18+4h).

Step 3: I then fill in the formula for the avg. rate of change to find the answer. [(18+4h) - 5] ÷ h.

Step 4: After simplifying, I get (13+4h) ÷ h.

---

Do I have a correct understanding of how to use the avg. rate of change formula and the coordinates P and Q? The reason that I am asking is because I explained this to my friend, and I just want to be sure that I explained it correctly. We're learning limits, and this equation was used.

To whomever answers this, thank you for taking the time to read this and to respond.

P.S. If there is one or two errors, please excuse me. It is late, and I really needed to post this before I forgot.

Your Q is incorrect.

4 * (2 + h) - 3 = 8 + 4h - 3 = 4h + 5

Thus:

[f(2+h) - f(2)]/[(x+h)-x] = [4h+5 - 5]/h = (4h)/h = 4