Question

Let f(x)=x^3-8(x). Calculate the difference quotient f(3+h)-f(3)/h
for
h=.1
h=.01
h=-0.1
h=-.1
If someone told you the derivative(slope of tangent line to the graph) of f(x) at x=3 was an integer, what would you expect it to be ?
(I'm confused in how to approach this problem, I know I can't just plug in the given h's into the diff.Quot. so would I plug in f(x) into h ? )

Answer 1

Would I start by pluging in my f(x) into the diff quotient ?

Answer 2

Yes, but first you need to make the necessary substitutions. Notice the first: f(3+h) means to replace all x's in your original f(x) with 3+h. Same goes for f(3), where all x's would be replaced with 3 in your original f(x).

Answer 3

Okay I'll try

Answer 4

So [(3+h)^3 -8(3+h) - (x^3-8x)]/h ?

Answer 5

The first part is correct. However, f(3) should just be a number, if f(3) is supposed to be there.

f(3) = (3)^3 - 8(3) = 9-24 = -15

Answer 6

That makes sense, but how I end up finding the values for the h's ?

Answer 7

Well I don't think your question asks you to find h, it's asking you to substitute each value of h into the difference quotient one-by-one.

Answer 8

Oh okay so I take the equation we came up with [(3+h)^3 -8(3+h) - (-15)]/h and plug in the h values right ?

Answer 9

Yup!

Answer 10

Oh okay let me see if I get it right :D thank you so much Pompeii00 !!!!!!:D

Answer 11

Not a problem. Let me know how ya do.

Answer 12

Just as clarification, notice f(3)=-15, make sure you incorporate that sign, so you'll actually have +15 in the difference quotient!!

Answer 13

So far the values I have gotten @Pompeii00 turned out wrong :O
for h=.1 I got 199.91
h=.01= 1819.0901

Answer 14

What values are you expecting for this problem?

Answer 15

I don't know its an online hw system :/

Answer 16

Are you certain that the question, equation, and values of h are correct?

Answer 17

yeah

Answer 18

Nope, that's what the actual question looks like

Answer 19

I've redone my math, I can't seem to figure out why the h values aren't working. At least from what I can see it makes sense. As for the derivative at x=3, i believe it to be 19. That's about it.

Answer 20

Oh okay thanks for your help anyways !

Answer 21

If anything comes to mind, I'll be sure to report it.

Answer 22

Oh okay thanks, I'll keep searching :/