Determine the highest real root of f(x) 5x^3 - 6x^2 + 11x + 6.1:

a. Graphically.
b. Using the Newton-Raphson method (three iterations, xo = 3.5).
c. Using the secant method (three iterations, x-1= 2.5 and xo = 3.5).
d. Using the modified secant method (three iterations, xo= 3.5, δ = 0.01).
e. Determine all the roots with MATLAB

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step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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step-by-step explanation: