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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

Consider the implicit relation x2+xy+y2=7.x^2+xy+y^2=7.
Total: 7 points

(a) Find dydx\frac{dy}{dx} in terms of xx and yy. (2 points)

(b) Find the slope of the tangent line at (1,2)(1,2). (1 point)

(c) Find the points on the relation where the tangent is horizontal. (2 points)

(d) Find the points on the relation where the tangent is vertical. (2 points)

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calc-ab.u5.t5-12.frq.001

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