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Free response·Hard exam skill (4/5)·No calculatorNeeds mentor review

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

Let q(x)=x2+1x+1,x≠−1.q(x)=\frac{x^2+1}{x+1},\quad x\ne -1.
Total: 6 points

(a) Find q′(x)q'(x) and simplify the numerator. (3 points)

(b) Find the tangent line to y=q(x)y=q(x) at x=1x=1. (2 points)

(c) Find all x-values where qq has a horizontal tangent. (1 point)

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