Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 01/Solution 1

The tangent line at $(A,f(A))$ crosses the x-axis at a point close to $z_{1}$, so starting at $x_{0}=A$ will approximate $z_{1}$ .

At $(B,f(B))$ the tangent line again crosses the x-axis at a point close to $z_{1}$, so $x_{0}=B$ is used to approximate $z_{1}$ too.

At $(C,f(C))$ the tangent line crosses the x-axis at a point close to $z_{4}$, this means that $x_{0}=C$ is a starting point to approximate $z_{4}$ .

The tangent line at $(D,f(D))$ crosses the x-axis at a point close to $z_{3}$, so starting at $x_{0}=D$ will approximate $z_{3}$ .

Answer: $\color {blue}z_{1},z_{1},z_{4},z_{3}$.