3. Consider the root-finding problem f(x) = 9x² ² - 4x/5= 0 for x = [-1,1]; see figure (b). (a) With xo = 0, compute x₁, x2 using Newton's method for approximating the solution to this problem. (b) With xo = 0 and ₁= -0.5, compute p2 using the Secant method to approximate the solution to this problem. (c) Based on the plot of f(x), for what choice of xo will Newton's method converge to the desired root? Make sure to motivate you answer.

Write down the general solution of 4x? – 2xy + 2 + (4y – x² + 2)y' = 0, x > 0, y > 0 You should express the solution implicitly, equating the polynomial expression to the arbitrary constant c (do not use capital c).

(c) Solve the following equation correct to 5 significant figures using Regula-Falsi Method.x3 +x2 +3x−4 = 0The root must be in the interval [0,1].(d) Solve the following equation correct to 5 significant figures using Bisection Method.x sin(2x) +e2x +3x−3 = 0The root must be in the interval [0,0.5].(e) [ The Method of Iteration ] Perform seven iterations to find a real root of the equationsy2 −5y+4 = 03yx2 −10x+7 = 0using the iteration method.(f) [ The Method of Iteration ] Perform seven iterations to find a real root of the equationsy2 −5y+4 = 03yx2 −10x+7 = 0using the iteration meth

6. Using Newton's method, find the root between 1 and 2. y=x²-x-1