given f(x) = -2x^6 - 1.5x^4 + 10x +2. use a root location technique to determine

Question

given f(x) = -2x^6 - 1.5x^4 + 10x +2. use a root location technique to determine the maximum of this function. perform iterations until the approximate relative error falls below 5%. if you use a braketing method use initial guesses of xl= 0 and xu= 1. if you use the newton raphson or the modified secant method, use an initial guess of xi= 1.if you use the secant method, use initial guesses of xi-1=0 and xi=1.assuming that the convergence is not an issue, choose the technique that is best suited for this problem. justify your choice.

Explanation / Answer

We can use Newton Raphson Method to find the value of the root. x_1 = x_0 - f(x_0)/f ' (x_0) To find the maximum of the given function,first we will differentiate the given function and find the root of that equation.therefore, f ' (x) = -12x^5 - 6x^3 +10 we get the root of the above equation at x=0.87 and f '(x) is positive when x< 0.87 and negative when x>0.87 Maximum value of the given function f (x) = -2x^6 - 1.5x^4 +10x+2 is at x=0.87 and is 8.97

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