Complete the following table for y = f(x) = 3x^2 and the...

Transcript

00:01 So in this question, we want to complete the following table for y equals f of x equals 3x squared and the indicated value of a equals 2.

00:12 So i'm looking at this expression here, and they're telling me my a is 2.

00:19 So i'm looking at f of 2 plus h minus f of 2 being divided by h.

00:29 So what is f of 2 plus h? my f of x is three x squared so what f of two plus h means is everywhere i see an x i replace it with the quantity of 2 plus h so f of 2 plus h this time is 3 times 2 plus h quantity square minus f of 2 of 2 well f of 2, what's that? well, that's 3 times 2 squared.

01:16 I'm plugging into f of x.

01:19 3 times 4, that's 12.

01:23 So 3 times 2 plus h quantity squared minus 12 being divided by h.

01:31 Now, i'm going to simplify this by expanding out the 2 plus h quantity square.

01:38 When i do, i get 4 plus 4h, plus h squared, this is minus 12, all being divided by h.

01:52 If i distribute that three, i've got 12, plus 12h, plus 3h squared, minus 12, being divided by h.

02:09 My 12s, they cancel out.

02:13 I'm left with 12h, plus 3h squared, being divided by h.

02:22 In the numerator, there is a, common factor of h, i can cancel that, or i can factor that out, leaving me with h times the quantity of 12 plus 3h divided by h.

02:37 Common factor of h in the numerator and denominator cancels out, i am just getting 12 plus 3h...

Question

complete the following table for y = f(x) = 3x^2 and the indicated value of a = 2 h | -0.1 -0.01 -0.001 -> 0 <- 0.001 0.01 0.1 (f(a + h) - f(a)) / h | ? ? ? -> ? <- ? ? ?

Question

complete the following table for y = f(x) = 3x^2 and the indicated value of a = 2 h | -0.1 -0.01 -0.001 -> 0 <- 0.001 0.01 0.1 (f(a + h) - f(a)) / h | ? ? ? -> ? <- ? ? ?

Please give Ace some feedback