How to Find the Average Rate of Change Over an Interval: g(x) = 3x2 − 2 on [x, x + h]

For the following exercises, find the average rate of change of each function on the interval specified for real numbers b or h.
g(x) = 3x2 − 2 on [x, x + h]
a(t) = 1/(t + 4) on [9, 9 + h]
b(x) = 1/(x + 3) on [1, 1 + h]

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[koiakro]

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[successfulworld]

Your channel is amazing, thanks a lot for those videos. You forgot to distribute the negative sign in the last step in the second question, the fina answer is -1 over 13(h+13). Keep going I am gonna watch all your videos before the final exams.

[fastlanegames]

Best tutorials on youtube thanks so much for creating these

[HectorAldana-vn]

I don't get the end of the second one. Wouldn't canceling h leave no numerator, so it would be 0, no?

[JerryTrade]

Is there a part 2 of this where you use those intervals to find average rates of given intervals on a table using the formula from your answer?

[kaisaai]

how do we get 2xh? i see you did the foil meathod but im not sure uf i understand, when i did (x+h)(x+h) i got X^2+xh+hx+h^2. Is xh and hx the same?