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{\bf 1.}  Search for zero
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Consider
$$
F(x)=\arctan{\left( 1/3(x^5 - 4 x^3 + 2x+1) \right)}-0.1
, $$

Solve the equation $ F(x)=0$ where
$$~~x\in [-2, 2] $$
by 

$\bullet$ bisection method 

$\bullet$ Newton method

$\bullet$ Secant method

Make 15 iterations.
Compare results after each iteration

Apply the same methods to the equation $ F(x)=0$ where
$$~~x\in [0.5, 1.5] $$


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\begin{quote}

\begin{center}
{\bf 2.}  Search for minimum
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Consider
$$
F_1(x)=\log (e^x -x -1 )/e^x + 3 ,  ~~ x \in[ -1,\, 10]
, $$ ~
$$
F_2(x) = \sqrt{(x-3)^4 + 0.05} ,  ~~ x \in[ 0,\, 5]$$~
$$
F_3(x)= (1/2) x^2 -x + \sin x, ~~ x \in [ 0.4]
$$
Find 
$$
x_0= \mbox{Argmin} F_i(x), ~~ F_i(x_0) $$

Apply

$\bullet$ Golgen section method 

$\bullet$ Newton method

$\bullet$ 3 points approximation method




Make 15 iterations.
Compare results after each iteration





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