Question $1$: We wish to solve $x^3-3x=4$ using Newton's method. Use $x_1=2$ as your initial approximation. Find $x_2,$ the next approximation. $($You are not being asked for the exact solution.$)$ Round your answer to three decimal places. Show your work. $(10$ pts$)$

a$)2\mathrm{.}196$

b$)2\mathrm{.}222$

c$)2\mathrm{.}302$

d$)2\mathrm{.}381$

e$)2\mathrm{.}411$

Question $2$: $f(x)=kx\frac{2}{k}$ for some constant $k.$ This function has a relative minimum at $x=1.$ What is the value of $k?$ Show your work. $(10$ pts$)$

a$)k=-2$

b$)k=-1$

c$)k=0$

d$)k=1$

e$)k=2$