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- You wish to minimize f(x)=10X(1^2 )-X_(2^2 ). If you use steepest descent starting at (1,1)will you reach the optimum in One iteration Two iterations More than two?2. Using the variation of parameters, find the particular solution of (D2+1)y=secxConsider finding an approximate solution to the nonlinear system of equations2x1 − x22 = 0,x1 + 0.77x2 = 1,where x(0) = 0.(a) Apply one iteration of the Newton method to obtain x(1)(b) Redo the previous part but by applying one iteration of the steepest descentmethod.
- Perform three iterations of the steepest ascent method to locate the maximum of f(x) = 3.5x + 2y + x^2 -x^4 +2xy-y^2 using initial guesses x = 0 and y = 0Use Newton-Raphson Method to find the approximate solution of the nonlinear equation f(x) giv en as x3-x-1=0.Use Euler's method with step size 0.5 to compute the approximate y-values, y1,y2,y3,y4 of the solution of the initial value problem,where y'=y-4x and y(3)=1