Core 3 Unit 8

Question 1

What is the sign change rule?

Answer 1

If f(x) is continuous for p≤x≤ q and f(p) and f(q) have opposite signs there is at least one root f(x)=0 between p and q

Question 2

How to do a decimal search?

Answer 2

Use the sign change rule to find p and q.
Then try and find p and q to another decimal place.
Repeat until the decimal place after what needs to be found, to check what it rounds to.

Question 3

How to find a root by iteration?

Answer 3

Rearrange equation so there is x= on one side and at least one x on the other side.
Define x0= for a suitable value and put this into the equation.
Use the ans button in place of this value to keep finding the next root.