Second Sufficient Condition for Local Extrema (Second Derivative Test)
Let f(x) have a second derivative at x₀, with f'(x₀) = 0 and f''(x₀) eq 0. - If f''(x₀) < 0, then f(x) has a local maximum at x₀. - If f''(x₀) > 0, then f(x) h…
Syllabus path: Functions › Preliminary Derivatives › Applications of Derivatives
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CSCA Mathematics Formula Reference
Formula and explanation
Let f(x) have a second derivative at x₀, with f'(x₀) = 0 and f''(x₀) eq 0. - If f''(x₀) < 0, then f(x) has a local maximum at x₀. - If f''(x₀) > 0, then f(x) has a local minimum at x₀. - If f''(x₀) = 0, this test is inconclusive; use the first sufficient condition or other methods.
Related tutorial and examples
Applications of Derivatives
Applications of Derivatives 1. Core Logic & Visualization The derivative f'(x) acts as a "barometer" for the function f(x), indicating its trend: Sign of f'(x) Monotonicity (Increasing/Decreasing) Zeros of f'(x) Extrema (Max/Min points) | Sign of f'(x) | Behavior of f(x) | Visual…
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