Question

For f(x) = ecos(x) use your graphing calculator to find the number of zeros for f '(x) on the closed interval [0, 2π].

a. 1
b. 2
c. 3
d. 4

Answer 1

@Babynini

Answer 2

\[e^{cosx}\] is that what it is?

Answer 3

Yes \[e ^{\cos \left( x \right)}\]

Answer 4

Ok so step one would be finding the derivative of that. Any ideas?

Answer 5

I tried using the chain rule but still it didn't give me any of the answers. the i tried d/dx

Answer 6

\[y=e^{\cos(x)}\] so i would take ln of both sides..

Answer 7

How would you do that?

Answer 8

\[\ln(y)=\ln(e^{\cos(x)})\] right?

Answer 9

and we just talked about how to solve the left side one.
so what does the left side equal? :)

Answer 10

Okay let me try that but it wants me to find the number of zeros for f(x) on the closed interval [0,2pie]

Answer 11

Well we need the derivative first though, because it wants the number of 0's for f'(x) not f(x)

Answer 12

I got -y sin(x)

Answer 13

Ya so \(f'(x) = -\sin(x)\cdot e^{\cos(x)}\)

Now use graphing calculator to graph \(f'(x)\) and count zeros.

Answer 14

Yeah! but y looks ugly there so plug in the original y
y =e^{cos(x)}

Answer 15

I think I did that wrong because I got 0 and that is not one of the answers

Answer 16

?? @Babynini

Answer 17

Is meaning zeros meaning how many times it crosses the x axis?

Answer 18

I believe so. The closed interval part [0,2pie] is throwing me off.

Answer 19

well here's the graph of it.
and 2pi= 6.2ish

Answer 20

That spot where it crosses x after the 6 is exactly 2pi

Answer 21

okay so 3 times?

Answer 22

yaya I think so:)

Answer 23

Okay thank you. Do you think you have time for one more to help me with?

Answer 24

I can try.

Answer 25

Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into the document.

Answer 26

This is what the problems/ numbers are