Question

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f ′(3.5).

Answer 1

x 3 4 7 10 13
f(x) 2 8 10 12 22

Answer 2

f(3.5) is in the middle of f(3) and f(4), so you do a simple average/mean equation. (2+8)/2=10/2=5

Answer 3

Alright, I got that, but I am unsure on how to get the derivative of it without an equation of some sort.

Answer 4

@ijakez

Answer 5

OH, didn't see the f prime!
My mistake!
It would be: since f(3.5) is in the middle of f(4) and f(3), you do:
[f(4)-f(3)]/(4-3)
which is (8-2)/1=6

Answer 6

How does that yield the f prime?

Answer 7

Wait, is that supposed to be change in y with change in x.

Answer 8

I don't think that would be it.

Answer 9

Wait, you were right, thanks! Do you mind answering another question?

Answer 10

f(x) and g(x) are a differentiable function for all reals and h(x) = g[f(3x)]. The table below gives selected values for f(x), g(x), f '(x), and g '(x). Find the value of h '(1).

Answer 11

x 1 2 3 4 5 6
f(x) 0 3 2 1 2 0
g(x) 1 3 2 6 5 0
f '(x) 3 2 1 4 0 2
g '(x) 1 5 4 3 2 0

Answer 12

@ijakez

Answer 13

I'm back! Give me a minute

Answer 14

Thank you!

Answer 15

I solved it and got 15. I am not sure if I am correct though.

Answer 16

My working was g'(f(3x)) x f'(3x) x 3
g'(2) x f'(3) x 3
5 x 1 x 3
15

Answer 17

How did you get g'(f(2))

Answer 18

I think I'm right, I'm going to try my answer.

Answer 19

Tell me how it goes!

Answer 20

I was right! thanks anyway though, your time was greatly appreciated!!!!

Answer 21

Sure, and great job!

Answer 22

I'd give you another medal, but I can't :(

Answer 23

All good! I'm in calc too, so I need as much practice as I can get!

Answer 24

Yeah, the AP exam is in a month!