Question

Find the slope of the function at the given value:
y=sin(2x) atx=−π

Answer 1

Find the derivative of the given function. Plug in x = -π

Answer 2

x = -pi .-.

Answer 3

I did the problem, but I am not sure where I went wrong

Answer 4

And we haven't gotten to derivatives yet

Answer 5

We are on slopes of tangent and secant lines and stuff like that. I understand it is similar to derivatives, but we haven't actually gotten there yet. We need to use the average and instantaneous rates of change stuff

Answer 6

This is asking for the slope at a specific point, which is instantaneous rate. Average rate would be the average rate of change between two points.
I'm not sure how to calculate instantaneous rate at a point without the derivative, I think.

Answer 7

Right, so thats the tangent line

Answer 8

Ohh, yes, yes. The slope of the line tangent to the function at x = -pi

Answer 9

yes

Answer 10

Its a kutasoftware problem : http://cdn.kutasoftware.com/Worksheets/Calc/04%20-%20Slope%20at%20a%20Value.pdf

Answer 11

Bleh. I wonder if there is a process I'm forgetting about.

Answer 12

It involves

Answer 13

The slope of the tangent line is equivalent to the value of the derivative at the same point.

Oh, ok, good. That's the limit definition of the derivative.

Answer 14

Ok

Answer 15

If you follow the definition of the derivative to your given function, applying the limit and such, you'll get the derivative. Then, you can plug in -pi for x.

Answer 16

I did. Idk where I went wrong. I got 0 instead of 2. I was hoping someone could show me how to do it

Answer 17

@girlover

Answer 18

Ok, so my problem comes down to lim (h->0) sin(2x)/x

Answer 19

How does that equal 2?

Answer 20

Can someone show me how they solved it? I keep messing up

Answer 21

@jim_thompson5910

Answer 22

Please, I have had this question up for like 2 hours

Answer 23

@Hero

Answer 24

@satellite73

Answer 25

@Ashleyisakitty

Answer 26

I'm assuming you mean at x=\(-\pi\)

Answer 27

yes

Answer 28

I accidentally left out the space

Answer 29

No problem, let me work this out right quick.

Answer 30

Thanks so much!

Answer 31

Im going to go to bed soon, so please ASAP

Answer 32

\(\frac{ð (y = sin(2 x))}{ð x} ~where~ x = -\pi\)
plug in
\(\frac{ð (y = sin(2 \times-\pi))}{ð -\pi}\)

\(y'(-\pi) = 2\)

Answer 33

It is blurring out the symbols

Answer 34

Refresh the page

Answer 35

ok

Answer 36

i dont understand what you did. we have to use the instantaneous rate of change formula

Answer 37

That was the best I could find as an explanation, I know it's no help; it's better than nothing, I suppose.

Answer 38

I appreciate it

Answer 39

@jim_thompson5910

Answer 40

lol 40 minutes until i can bump

Answer 41

I have to go to bed, i will respond in the morning.