AC derivative-point-picking
Solve high-school or college-entrance-exam style derivative problems centered on root existence, root count, and parameter ranges. Use when a problem asks whether a function has roots/intersections, exactly how many roots it has, or which parameters make roots exist. The skill analyzes with derivatives, monotonic intervals, extrema, limits, and value ranges, then rewrites the final proof using concrete point selection, sign changes, continuity, and the intermediate value theorem. In teaching mode, explain where chosen points come from using tangent bounds, exponential/log inequalities, Taylor-style estimates, quadratic fitting, homomorphic transformations, or explicit threshold solving.
As a process C 55/100 · Has gaps — weak spots: result and completion, when it triggers, inputs and preconditions
How to improve
- Your own cases (evals/evals.json, 4–6 real requests with expected answers): the full check would then run those instead of a model-drafted suite.
- A spec.yaml with trigger phrases and assertions — a behaviour contract for CI; `skilltest init` writes a template.
Guard findings · 0
✓ No critical or high findings
Files scanned: 10. Evidence is masked. Grey chips explain why severity was lowered.
Against the Agent Skills spec
✓ No remarks against the Agent Skills spec
Process rating: all ten parameters 55/100
- 0Result and completion. Does not say what the result is
- 0Inputs and preconditions. Does not say what the process needs to start
- 20When it triggers. No condition that starts the skill
- 60Tools and files. Uses tools (bash) that frontmatter does not declare
- 70Failures and branches. 4 branches
- 100Steps. 86 steps
- 100Consistency. Name and required fields are in place
- 100Execution cost. Instruction body is 1977 tokens
- 100Running it twice. No mutating operations
- 100Progress reporting. Reports progress
Everything here is measured from the skill text rather than judged by a model, so the numbers are checkable. A parameter weighs more when it is a more common reason for the process to stall.
Quality signals
- +5Description has no quoted example phrases that should trigger the skill
- +4Description does not say when NOT to use the skill (false activations)
- +3Output format is not stated: the model decides each time
- +1No license
- +2Single-language instructions
- +3Description length 695: enough signal without eating the budget
- +4Structure: 18 headings
- +3Step-by-step instructions: 86 items
- +4Has examples (0 code blocks)
Quality base 70; lint remarks subtract, signals add up to 100. Result: 84.