Determine the highest real root of f (x) = x3 − 6x2 + 11x − 6.1: (a) Graphically. (b) Using the Newton-Raphson method (three iterations, x0 = 3.5 (c) Using the secant method (three iterations, x−1 = 2.5 and x0 = 3.5). (d) Using the modified secant method (three iterations, x0 = 3.5, δ = 0.01). (e) Determine all the roots with MATLAB.

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step-by-step explanation:

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4