In Newton Raphson method, if the curve 𝑓(𝑥)f(x) is constant then ________.a)None of the mentionedb)𝑓′(𝑥)=0f ′ (x)=0c)𝑓(𝑥)=0f(x)=0d)𝑓′(𝑥)=𝑐f ′ (x)=c
Question
In Newton Raphson method, if the curve 𝑓(𝑥)f(x) is constant then ________.a)None of the mentionedb)𝑓′(𝑥)=0f ′ (x)=0c)𝑓(𝑥)=0f(x)=0d)𝑓′(𝑥)=𝑐f ′ (x)=c
Solution
The Newton-Raphson method is a root-finding algorithm that uses the first derivative of a function. The method starts with a function f defined over the real numbers x, an initial guess x0 for a root of f, and the derivative f ′ of f.
If the curve f(x) is constant, it means that the function f does not change as x changes. In other words, the slope of the function is zero at all points.
Therefore, the derivative of the function f, denoted as f'(x), is equal to zero.
So, the correct answer is b) f'(x) = 0.
Similar Questions
The Iterative formula for Newton Raphson method is given by __________a)𝑥(1)=𝑥(0)+𝑓′(𝑥(0))𝑓(𝑥(0))x(1)=x(0)+ f(x(0))f ′ (x(0)) b)𝑥(1)=𝑥(0)−𝑓(𝑥(0))𝑓′(𝑥(0))x(1)=x(0)− f ′ (x(0))f(x(0)) c)𝑥(1)=𝑥(0)+𝑓(𝑥(0))𝑓′(𝑥(0))x(1)=x(0)+ f ′ (x(0))f(x(0)) d)𝑥(1)=𝑥(0)−𝑓′(𝑥(0))𝑓(𝑥(0))x(1)=x(0)− f(x(0))f ′ (x(0))
The Newton Raphson method is also called as ____________a)Chord methodb)Diameter methodc)Secant methodd)Tangent method
The basic Newton method is used for the solution of nonlinear problems
Question 2 5 MarksFind a root of the following equation in the interval (0,1) using Newton-Raphson Method after threeiterations𝑥𝑒𝑥 − cos 𝑥 = 0Take Initial value 0.5.Note: Accuracy up to four decimal places is required. Here is a transcendental equation all thecalculation should be done in the radians mode.
Suppose a curve 𝑦(𝑥) has the derivatived𝑦d𝑥=5−2𝑥.1. Find 𝑦 in terms of 𝑥.𝑦(𝑥)=
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