Task $5.$Please read the instructions in detail. Write everything that is required in the task clearly and legibly. Write as simple and understandable code as possible WITH COMMENTS WITH THE CODE. Begginer friendly to solve the task.$$

Write scripts in Matlab with algorithms that solve a nonlinear equation with one unknown using the following methods:

Function: f$($x$)=2*$x$4-15*$x$2+5*$x $+5$

$$Interval: $[0,2]$

Tolerance: $1$e$-12$

$$Maximum number of iterations: $100$

$1.$Secant method $,$ initial parameters: Interval: $[0,2]$

plot this

Scripts should print: PLEASE PRINT ALL ITERATIONS, NOT ONLY IF ITs CONVEREGNTED

a$)$the solution, i$.$e$.$the zero$-$point x$0->$ THIS IS ONE PRINT

b$)$f$($x$0)->$ THIS IS ONE PRINT

c$)$the required number of iterations until convergence to the given tolerance with a corresponding message. $->$ THIS IS ONE PRINT

d$)$If convergence is not achieved within the given maximum number of iterations $->$ this is one print $(100),$it is necessary to print the last value of the solution x$0$and f$($x$0),$along with a corresponding message.

$2.$Fixed point method.

In the same code it needs to be check left$($x $=0)$ and right$($x$=2)$ convergence.

plot this

Function: f$($x$)=2*$x$4-15*$x$2+5*$x $+5$

$$Interval: $[0,2]$

Tolerance: $1$e$-12$

$$Maximum number of iterations: $100$

Scripts should print: PLEASE PRINT ALL ITERATIONS, NOT ONLY IF ITs CONVEREGNTED

a$)$the solution, i$.$e$.$the zero$-$point x$0->$ THIS IS ONE PRINT

b$)$f$($x$0)->$ THIS IS ONE PRINT

c$)$the required number of iterations until convergence to the given tolerance with a corresponding message. $->$ THIS IS ONE PRINT

d$)$If convergence is not achieved within the given maximum number of iterations $->$ this is one print $(100),$it is necessary to print the last value of the solution x$0$and f$($x$0),$along with a corresponding message.

$.$

FINAL:

MUST ATTACH TO SOLUTIONS:

a$)$Printing of Matlab program code from scripts with comments

b$)$Printout of results and tabular comparison of default methods and launch variants.

$6.$Conclusion $-$MUST WRITE WHAT THE USED METHODS PROVIDED AS A RESULT.