Use the bisection method to find the minimum of the function is $f(x)= 3x^2–4x+1$ over the interval $[0,2]$ . Determine the optimal value of $x$ within $5\%$ of the initial interval and How many function evaluations are needed to get within x* ± 0.001?
The first iteration $a=0,b=2, m=(a+b)/2=1$
$f(a)=1, f(b)=5, f(m)=0$
I do not understand what the first part question is asking.Is it mean that I need to continue the evaluation until I find the value of $b-a$ is closed to $0.05$? After the 11 evaluations , I get a=0.3321 and b=0.3341.But x*=0.6667 instead of 0.3333