Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Question
(a) Find the slope of the solution curve through at that point. (1 point)
(b) Write the equation of the tangent line to the solution curve through . (1 point)
(c) Explain why any solution curve has horizontal tangent wherever it crosses the line . (2 points)
(d) At , state whether the solution is increasing or decreasing and justify. (1 point)