- #1

jaqueh

- 57

- 0

## Homework Statement

Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3]

## The Attempt at a Solution

I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter jaqueh
- Start date

- #1

jaqueh

- 57

- 0

Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3]

I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

- #2

Dick

Science Advisor

Homework Helper

- 26,263

- 620

Check some obvious values in between -1 and 3. Maybe x=0 and x=2? You are giving up too easily.

- #3

pasmith

Homework Helper

- 2,333

- 937

## Homework Statement

Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3]

## The Attempt at a Solution

I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

You can find f'(x) analytically, so maybe you should do that and then apply the intermediate value theorem.

- #4

jackmell

- 1,804

- 53

## Homework Statement

Show f(x)=(x−2)sinxln(x+2) has f'(x)=0 somewhere on [-1,3]

## The Attempt at a Solution

I tried using Rolle's theorem, but f(-1)≠f(3). Then I tried the mean value theorem, but didn't get 0 either.

Well if it's numerical analysis, why are you using those theorems? Suppose it was some function that you didn't even know what the form was, how could you show the derivative is zero somewhere in that interval? If it was mine, I'd generate "numerically" since this is numerical analysis, a set of equally spaced points in that interval and then compute the value of the function and then I'd inspect the list for the "monotonicity" change, that is, when the numbers are increasing then decreasing or vice-a-versa. However if there is an inflection point, the derivative could still be zero without this change in monotonicity. But we could at least rule out the former case this way. Anyway, lots of tough problems won't give you the luxury of using nice theorems and you'll have to muscle-through the data in this way or another.

I got an idea, why don't you write a short Mathematica program to generate these numbers then pick out the monotonicity change?

- #5

jaqueh

- 57

- 0

- #6

- 9,568

- 774

What does the interval [0,1] do for you?

- #7

jaqueh

- 57

- 0

What does the interval [0,1] do for you?

sorry i meant for the interval to be [0,2]

then i get f(0)=f(2)=0 => rolle's

Last edited:

- #8

- 9,568

- 774

sorry i meant for the interval to be [0,2]

then i get f(0)=f(2)=0 => rolle's

That's better.

Share:

- Replies
- 1

- Views
- 197

- Replies
- 15

- Views
- 466

- Last Post

- Replies
- 5

- Views
- 497

- Last Post

- Replies
- 28

- Views
- 571

- Last Post

- Replies
- 8

- Views
- 546

- Last Post

- Replies
- 1

- Views
- 260

- Last Post

- Replies
- 7

- Views
- 312

- Replies
- 19

- Views
- 422

- Last Post

- Replies
- 31

- Views
- 920

- Replies
- 9

- Views
- 361