Verify that the root of the equation \( x^{3}-3 x+1=0 \) lies between 0 and 0.8 . Then use bisection method to find to four decimal places the root of the equation.
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8. Evaluate the function \( f(x) = x^3 - 3x + 1 \) at the endpoints of the interval [0, 0.8]: \[ f(0) = 0^3 - 3(0) + 1 = 1 \] \[ f(0.8) = (0.8)^3 - 3(0.8) + 1 = 0.512 - 2.4 + 1 = -0.888 \] Since \( f(0) = 1 \) and \( f(0.8) = -0.888 \), and because the function Show more…
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