differentiability
Having a tangent
Differentiability is the property of being differentiable—in calculus, capable of having a derivative calculated at a given point.
A function is differentiable where its graph has a definite slope, meaning it's smooth enough to draw a tangent line.
Corners, cusps, and discontinuities break differentiability: The function is continuous everywhere but differentiable nowhere.
Without pause or gap
- smoothWithout roughness or difficulty
- analyticExamining by decomposition
- piecewiseMulti-rule function definition
- cuspPoint of transition
corner · kink · discontinuity · singularity · regularity · boundedness · uniform · nowhere
Function's rate of change
- gradientRate of change across space
- HessianGerman soldier-for-hire, 1770s
- tangentLine touching curve once
- slopeAngled terrain or steepness
limit · partial · implicit · parametric · directional · linearization · infinitesimal · Leibniz
Demonstrated logical conclusion
- proofDemonstration of truth
- rigorStrict, thorough precision
- existenceState of being real
- uniquenessQuality of being singular
necessary · sufficient · condition · domain · range · interval · neighborhood · open
Outward-curving quality
- concavityInward-curving surface quality
- extremumFunction's boundary value
- constraintLimiting condition or rule
- nonsmoothUneven in texture
convergence · backpropagation · objective · feasibility · descent · ascent
continuous
Without pause or gap
- smoothWithout roughness or difficulty
- analyticExamining by decomposition
- piecewiseMulti-rule function definition
cusp · corner · kink · discontinuity · singularity · regularity · boundedness · uniform · nowhere · pathological
derivative
Function's rate of change
- gradientRate of change across space
- HessianGerman soldier-for-hire, 1770s
- tangentLine touching curve once
slope · limit · partial · implicit · parametric · directional · linearization · infinitesimal · Leibniz · Newton
theorem
Demonstrated logical conclusion
uniqueness · necessary · sufficient · condition · domain · range · interval · neighborhood · open · closed
convexity
Outward-curving quality
- concavityInward-curving surface quality
- extremumFunction's boundary value
- constraintLimiting condition or rule
nonsmooth · convergence · backpropagation · objective · feasibility · descent · ascent
differentiabilitydiscontinuity
Break in continuity
jaggedness · singularity · irregularity · corner · cusp
differentiabilityindistinguishability
State of being identical
sameness · uniformity · homogeneity · identity · equivalence
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