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Change of Sign Method If we let f(x)?3x³-0.5x²-0.5x-1, in order to solve this equation and determine its roots, it is necessary for it to be written in the form 3x³-0.5x²-0.5x-1=0. The root of the equation f(x)=0 is indicated where y=f(x) crosses the x-axis. Roots of the equation 3x³-0.5x²-0.5x-1=0, will be found to a three decimal place accuracy. Having illustrated the equation graphically using Autograph, it is evident that the equation has only root that lies between the interval [0,1]. Before proceeding, it is necessary to check that there is a sign change in the above interval: f(0) = 0-0-0-1= -1 f(1) = 3-0.5-0.5-1 =1 The method that will be used for the numerical solution of the equation is the decimal search method. I will first take the increments in x of size 0.1 within the interval [0,1], calculating the value of the function 3x³-0.5x²-0.5x-1 for each one, until a change of sign is found. x 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 f(x) -1 -1.052 -1.096 -1.114 -1.088 -1 -0.832 -0.566 -0.184 0.332 The above table illustrates...

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