Diagnostic — checks Unit 2 derivatives + Unit 1 limits-at-infinity prereqs
📋 Not Graded — Teacher Feedback
Purpose: Confirms readiness to perform full curve analysis. Probes derivative computations and limit behaviour at infinity.
Q1 Prereq — Derivatives
[3]
For \(f(x)=2x^3-9x^2+12x\), find \(f'(x)\) and solve \(f'(x)=0\).
Q2 Prereq — Sign analysis
[3]
Determine the sign of \(g'(x)=(x-1)(x-4)\) on each interval. State whether \(g\) is increasing or decreasing.
Q3 Prereq — Asymptotes
[3]
For \(h(x)=\dfrac{2x^2-3}{x^2-1}\): a) state vertical asymptotes; b) find horizontal asymptote; c) state domain.
Q4 Thinking
[3]
A function \(f\) is given with \(f'(2)=0\) and \(f''(2)=-4\). What does this tell you about \(f\) at \(x=2\)? Justify.
Q5 Communication
[3]
Explain in your own words the difference between a critical point, a local extremum, and an inflection point. Include the role of \(f'\) and \(f''\).
Q6 Thinking
[3]
A graph of \(f'(x)\) is described as: positive on \((-\infty,-1)\), zero at \(-1\), negative on \((-1,2)\), zero at \(2\), positive on \((2,\infty)\). Sketch (in words) and locate all extrema of \(f\).
Q7 Reflection
[2]
What aspect of curve sketching feels most overwhelming — analyzing derivatives, finding asymptotes, or combining everything into a sketch?
📝 Teacher Feedback
Your teacher will provide feedback after reviewing.