The extremum (minimum or maximum) point of a function f(x) is to be determined by solving $$\frac{{{\text{df}}\left( {\text{x}} \right)}}{{{\text{dx}}}} = 0$$   using the Newton-Raphson method. Let f(x) = x³ - 6x and x₀ = 1 be the initial guess of x. The value of x after two iterations (x₂) is

What is the cube root of 1468 to 3 decimal places?

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson's rule is

Angle (degree)	0	60	120	180	240	300	360
Torque (Nm)	0	1066	-323	0	323	-355	0

Roots of the algebraic equation x³ + x² + x + 1 = 0 are

In the Newton-Raphson method, an initial guess of x₀ = 2 is made and the sequence x₀, x₁, x₂ ... is obtained for the function 0.75x³ - 2x² - 2x + 4 = 0
Consider the statements
I. x₃ = 0.
II. The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?