Solve both parts and justify the conditions used. Part A: A learner fits a straight line through two observations and claims the model is valid forever. Evaluate the claim. Part B: Find the greatest value on the stated closed interval.
- Use the domain, units and sampling assumptions stated in the question.
- Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Hint 2
Worked solution
Part A reasoning
Define the variable and its units, form a model, and check feasible inputs.
Check further observations and the mechanism generating the data; state a justified range of use.
A model is conditional on assumptions and evidence.
Part B reasoning
Identify the input domain, rule and requested output before substituting.
Calculate or simplify this relation.
The greatest distance from the vertex determines the maximum here.
A: Two observations determine a line but do not validate unlimited extrapolation. B: The requested value is 9.
Checks and common pitfalls: A model is conditional on assumptions and evidence. The greatest distance from the vertex determines the maximum here.
Reasoning checklist · self / teacher assessment
- Solve part A with its stated restrictions.
- Solve part B using an appropriate representation.
- Give the reasoning and check conditions in both parts.
Think first. Reveal a hint when the class is ready.