How this calculation works
Classify a stationary point using the two-variable second derivative test.
THE FORMULA
D=fₓₓ fᵧᵧ−fₓᵧ²A worked example
Curvatures 2 and −2 with zero mixed derivative give determinant −4 and a saddle.
Good to know
The gradient must vanish at the point. A zero determinant is inconclusive.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Classify a stationary point using the two-variable second derivative test.
The primary result is labeled “Classification”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The gradient must vanish at the point. A zero determinant is inconclusive.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
Curvatures 2 and −2 with zero mixed derivative give determinant −4 and a saddle.
Which rule does this calculator apply?
D=fₓₓ fᵧᵧ−fₓᵧ²