Formulae: Bisection method $x_m=\frac{x_i+x_n}{2},$ Newton$-$Raphson method $x_{i+1}=x_i-\frac{f(x_t)}{f^{\text{'}}(x_t)}$

Problem$-1$: For a merchant, the profit on a product is a function of the oost $f$ the product $($x$),$

which can be expressed as:

Profit: $,f(x)=-2x^6-1\mathrm{.}5x^4+10x+2$

Find the cost of the product for the maximum profit to the merchant. Assume $x_1=0$ and $x_{||}=1$

$($a$)$ Use the bisection method, and perform $5$ iterations

$($b$)$ Use Newton$-$Raphson method to perform $5$ iterations

$($c$)$ If the true solution of the problem is $0\mathrm{.}8714.$ calculate and discuss error trends in part $($a$)$

and $($b$)$