💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# Use Newton's method to find all solutions of the equation correct to six decimal places.$3\cos x = x + 1$

## $x \approx-3.637958,-1.862365,0.889470$

Derivatives

Differentiation

Volume

### Discussion

You must be signed in to discuss.
MB

Martin B.

April 8, 2020

Could you please take the time to explain how you got the initial value of x?

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp

### Video Transcript

Okay. We know we take the derivative, which is F Prime of X is negative. One minus three side of X. We know ex of one is negative. 3.7. This could be our initial approximation. Then we know exits to plugging into Newton's formula. We get negative. 3.63 we know except three is negative. 3.63 And except for his negative 3.63 acts of five repeating the same processes negative. 3.63 which gives us X is approx more negative. 3.63 7957 We could do the same process with extra ones. Negative. 1.9 we get. AKs is 1.8. Sex acts of one is one. We access approximately zero point a nine 470

#### Topics

Derivatives

Differentiation

Volume

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

##### Michael J.

Idaho State University

Lectures

Join Bootcamp