Question

How do I do find two values for this question?

Answer 1

Consider the graph of \[y = x+2\cos(x)\] for \[x \in [0, \pi]\]What are the exact values at which the curve have horizontal tangents?

Answer 2

I'm guessing I'm going to have to find the derivative first, so I got \[1 + -2 \sin (x) = y\] I set y to 0 in order to get a horizontal slope, which I got .5235987798 as one of the values where my tangent line is horizontal. How do I get the next value?

Answer 3

1- 2sinx=0
2sinx =1
sinx=1/2
So two values of x possible in (0,Π)

Answer 4

Do you understand it?

Answer 5

That was the answer I got, but that's only one value.

Answer 6

Sinx = 1/2
So x=Π/6 and x=5Π/6

Answer 7

How do you find that with steps though?

Answer 8

Look at the graph for inspiration.

Answer 9

To get the x-values, you would look for relative maximum or minimum within the restricted domain.

You took the first derivative equation and set it to zero.

When you did that, did you get the two answers of pi/6 and 5*pi/6 ?

Answer 10

lol I think I'm just having issues finding all values of x between 0 and pi that equal 1/2. Like I don't remember how to do that.

Answer 11

1 - 2* sin(x) = 0

-2* sin x = -1

sin x = 1/2

x = pi/6 and x = 5*pi/6 [0, pi]

Answer 12

Plot y=sinx
Then , draw a line y=1/2
And find point of intersection of the two in (0,Π/2)

Answer 13

Sorry (0,Π) not (0,Π/2)

Answer 14

I got the 0.523... thing, which I converted by dividing it by pi. so pi/6. But I completely forgot how to get the 5pi/6.

Answer 15

0? idk o_O

Answer 16

I used arcsin to find pi/6

Answer 17

Why don't you use the graph?

Answer 18

How do I use the graph?

Answer 19

Do you know the graph of Sinx..

Answer 20

If you learned about the unit circle when you began to study trig, you might recall something like this.