Question

Calculus check 3 help with 2.

Answer 1

1 B
2 Need help
3 need help
4 C
5 A

Answer 2

@mathmale

Answer 3

Any thoughts about what you might do in regard to solving #2? Note that

dy/dx = 3sin x is a formula for the slope of the curve y= f(x) at any given x.

Assume that x is the angle measured in radians, at least for now.

Answer 4

so take the derivative of 3 sin x?

Answer 5

No. 3 sin x is already your derivative. Taking the derivative of 3 sin x would give you a formula for the 2nd derivative of the unknown function y=f(x).

dy/dx = 3 sin x. What would the slope of the tangent line to that f(x) be at x = 0 ?

At x = pi / 6 ?

Answer 6

so 3 sin (0)?

Answer 7

yes, and what is the value of sin 0?

Answer 8

0

Answer 9

Yes, so what is the slope of f(x) at x=0?

Answer 10

hmmm so slope of 3 sin x at (0,0)?

Answer 11

I know at (0,1) the slope is 3 which would be y=3x and parallel right?

Answer 12

So 2 would be a?

Answer 13

The slope of f(x) (or of the graph of y) at x=0 is just 0. No reason to write out (0,0). We are concerned about the behavior of f(x) and the value of the slope of the graph of f(x) at (0,1). At (0,1), what is the slope of the tangent line?

Answer 14

3
(See above)

Answer 15

But you've said that sin 0 = 0. There's no '3' in the picture for this particular x value.

Answer 16

So, what do you know about the tangent line to f(x) that goes thru (0,1)?

Answer 17

not sure. I'm confused.

Answer 18

I, too, found this problem to be a bit confusing.
Still, if you let x=0, sin x=0, and 3sin x=0, and thus the tangent like through (0,1) has a slope of zero.

Answer 19

Yeah when I asked zep about it he said did they mean (1,0)???? So the best choice would be A?

Answer 20

We don't have a choice about that. We are asked to describe the slope field at the given point (0,1).
Let me look again at the several answer choices. You do the same.

Answer 21

ok

Answer 22

Should we continue to consider D further or should we toss it out? Why?

Answer 23

We should toss it out because it is asking for the slope field of (0,x)) right?

Answer 24

I would toss it out also, but for a very different reason: We know little or nothing about the graph at (3,0) and have no business being on the x-axis (y=0).

Consider whether we could eliminate any of the other 3 answer choices, after elim. D.

Answer 25

I would elim B because it is asking about (0,3) but the question is asking for at (0,1)

Answer 26

So then we are looking to find it it is parallel or perpendicular at that point (either a or c)

Answer 27

that makes sense to me. What other alternative answers are left?

Answer 28

A and C so we need to find if parallel or perpendicular.

Answer 29

From our previous discussion, does it seem to you that the tangent line to the curve of f(x) is parallel to or perpendicular to y=3x? Why?

Answer 30

Perpendicular because it has a slope of 0 so it runs horizontally to the other line. So C!

Answer 31

If you were to choose C, your slope field would consist of short lines running up and down. Does that sound right? What would be the alterantive?

Answer 32

No it doesn't slope fields usually run horizontally so it would be A!

Answer 33

Also in regard to C: You'd have some vertical tangent lines.

Yes. You've done a good job of elimination and of reasoning through your choice of the remaining possible answers.

Answer 34

Thanks I have 1 more question. I will close this one and open a new fresh clean one. :)

Answer 35

Slope fields can, buty don't often, "run horizontally." Typically, you'll see slopes of 1/4, 1/2, 1, 2, and so on but not of much larger numeric values.

Answer 36

OK.