4.2 Differential: Newton' Method Q1) Grade :12 Newton's Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval. $3 - 12x - 4x^3 - 3x^4 = 0$ in $[-3, -1]$ Q2)
Added by Erica H.
Close
Step 1
The derivative of 3-12x-4x^3-3x^4 is -12-12x^2-12x^3. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 97 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the indicated root of the given equation to at least four decimal places by using Newton's method. 3x^3-6x^2-x-1=0; between 2 and 3 Hint: Do not assume first value of x exactly between 2 and 3 (=2.5); first determine if the root is closer to 2 or to 3 and then choose first value of x accordingly; it will save you few iterations of Newton's procedure. Examples of anwser: 3.4560, -1.1852
Adi S.
(a) Use Newton's method with $x_{1}=1$ to find the root of the equation $x^{3}-x=1$ correct to six decimal places. (b) Solve the equation in part (a) using $x_{1}=0.6$ as the initial approximation. (c) Solve the equation in part (a) using $x_{1}=0.57 .$ (You defi- nitely need a programmable calculator for this part.) (d) Graph $f(x)=x^{3}-x-1$ and its tangent lines at $x_{1}=1$ $0.6,$ and 0.57 to explain why Newton's method is so sen- sitive to the value of the initial approximation.
Applications of Differentiation
Newton's Method
(a) Use Newton's method with $\mathrm{x}_{1}=1$ to find the root of the equation $\mathrm{x}^{3}-\mathrm{x}=1$ correct to six decimal places. b) Solve the equation in part (a) using $x_{1}=0.6$ as the initial approximation. (c) Solve the equation in part (a) using $x_{1}=0.57 .$ (You defi- nitely need a programmable calculator for this part.) (d) Graph $f(x)=x^{3}-x-1$ and its tangent lines at $x_{1}=1$ $0.6,$ and 0.57 to explain why Newton's method is so sen- sitive to the value of the initial approximation.v
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD