Question

TIMED TEST- I am so lost, I've never seen this before HELP

f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the value of g ′(0.2)?



x, 0.1, 0.2, 0.3, 0.4, 0.5
f ′(x) 1 2 3 –4 5

Answer 1

f is the same as g except that in g, x is multiplied by 2.
This produces a result called "horizontal compression." It's like you start with a pillow and compress it horizontally to half its previous length.

for example, the graph of sin x has a period of 2pi.
But the graph of sin (2x) has a period of half that, or just pi.

Horizontal compresion!

Answer 2

My options are 2, -8, 4, or can't be determined

Answer 3

Hints:
The derivative of f(x) at 0.2 is 2, according to the table.
The derivative of f(2x) at 0.2 is half that.
Please look up "horizontal compression in graphs."

Answer 4

Then wouldn't the answer be 1?

Answer 5

Note that the sine function (used as an example) is differentiable everywhere.

Could you graph the sine function, sin x, on the interval [0,1]?
Next, graph sin 2x and compare your results.

Next, calculate and draw in the slope of the sin x function at x=0.2.
Finally, as a final check, calculate and draw in the slope of the function sin 2x at x = 0.2

This would help you to confirm your first answer choice ( 1 ).

Answer 6

That doesn't make any sense to me...

Answer 7

Intuitively it seems that the slope of the sine function increases if you compress the graph horizontally by a factor of 2.

If you have a graphing calculator, graph sin x and sin 2x on the same set of axes on the interval [0, 1]. The latter has a steeper slope than the former at x=0.2.

Answer 8

Okay, that makes sense when you look at the graph, but how does that help me with this since it is a table?

Answer 9

I'd rather not go too far into that suggestion of mine if it doesn't make any sense to you.
Do you have any better idea of how to respond to this question than when you started?

Remember that a graph is often plotted from a table, and that a rough table can be made up from data from a graph. So they're just different ways of presenting the same info.

Answer 10

If you don't understand or don't want to work with f(x)=sn x as an example,
then let f(x)=x and g(x)=f(2x)=2x. Graph f=x and g=2x. Compare their slopes.

Answer 11

I understand that part

Answer 12

Good. have you any specific question for me at this point?

Answer 13

How does that help me with this table?! Obviously the answer isn't "d" or "b", am I correct for assuming that?

Answer 14

I'd like to get some rationale from you on the choices you've eliminated (how is it obvious that the answer isn't "d" or "b"?) and the two you've not eliminated ("a"
or "c")?

Let me ask you this: Suppose f(x) is defined as f(x)=2x (which is definitely differentiable everywhere) and g(x)=f(4x). which one has the greater slope? And what are the two slopes?

Answer 15

Can you differentiate my f(x)/ my g(x)?