Find the maximum of $()=41\mathrm{.}82+1\mathrm{.}230\mathrm{.}34$ using:

a$)$ The Golden$-$section search with $=2,=4,=1\%$

Calculate the first iteration in Excel or by hand and then solve the problem in Matlab.

Hint: after iteration $1,$ the estimate of the maximum is $(1\mathrm{.}7082,5\mathrm{.}0075)$ and approximate $\%$ error is

$134\mathrm{.}16\%.$ After iteration $1,$ the estimate of the maximum is $(2\mathrm{.}5836,5\mathrm{.}6474)$ and approximate $\%$ error

is $54\mathrm{.}82\%.$ It should take $10$ iterations.

b$)$ Newton$$s method with $=,=\%$

Calculate the first iteration in Excel or by hand and then solve the problem in Matlab.

Hint: It should take $4$ iterations