I have 2 questions that I couldn't figure out

Could you please explain me below questions

Question 1

Consider the functionf(x)=ax2+bx+1 where a and b are constants. Describe the critical points and possible points of inflection for f in terms of a and b

Question 2

Why does Newton's Method fail in finding a root off(x)=x33x2+x+3 when x₀ =1 ?