Question

PLEASE HELP
find the average rate of change of f(x) = 3x^2 + 1
(a) from 2 to 4
(b) from -2 to 0
and
(c) from 2 to 5

Answer 1

Always, it is this: \(\dfrac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\)

You are given the x-values. Substitute and calculate!

Answer 2

so 4-2 and divide? I am confused..

Answer 3

4-2 is the first denominator. You must also calculate the numerator, f(4) - f(2).

Answer 4

so the denomiator is on the bottom?

Answer 5

So how would I put it into an answer? 2,2?

Answer 6

You should know your numerator from your denominator.

f(4) = 49
f(2) = 13

a) (49-13)/(4-2) -- Almost done.

Answer 7

how did you get 49 and 13?

Answer 8

I am sorry I am not good at this

Answer 9

You need to know how to use function notation.

What does this mean? g(x) = 3x-4

If I ask for g(4), what does that mean? How does that notation work?

I am quite worried about this. How dod you manage to get this close to calculus without encountering function notation? Very odd.

Answer 10

plug 4 for x?

Answer 11

We do like to call it "substitute", but that's the idea. What do you get for g(4)?

Answer 12

I don't know... I am sorry I am embarrassed

Answer 13

Yousaid yourself, sort of, substitute x = 4.

If g(x) = 3x - 4, then g(4) = 3(4) - 4 = 12 - 4 = 8
g(9) = 3(9) - 4 = 27 - 4 = 23

Do you see how this works? You ARE going to have to review some algebra.