Minimize f (x) = x4 − x + 1 using secant method with initial points x−1 = 3 and x0 = −3

To minimize the function f(x) = x^4 - x + 1 using the secant method, we start with two initial points x-1 = 3 and x0 = -3.

Step 1: Calculate the function values at the initial points. f(x-1) = (3)^4 - 3 + 1 = 73 f(x0) = (-3)^4 - (-3) + 1 = 79

Step 2: Calculate the next point using the secant method. x1 = x0 - (f(x0) * (x0 - x-1)) / (f(x0) - f(x-1)) x1 = -3 - (79 * (-3 - 3)) / (79 - 73) x1 = -3 - (-474) / 6 x1 = -3 + 79 x1 = 76

Step 3: Calculate the function value at x1. f(x1) = (76)^4 - 76 + 1 = 416413

Step 4: Repeat steps 2 and 3 until the desired accuracy is achieved. x2 = x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0)) f(x2) = (x2)^4 - x2 + 1

Continue this process until the function value is minimized to the desired accuracy.