Necessary Condition for Local Extrema (Fermat's Lemma)
If the function f(x) is differentiable at x₀ and has a local extremum (maximum or minimum) at x₀, then f'(x₀) = 0. Note: Points where the derivative is zero ar…
Syllabus path: Functions › Preliminary Derivatives › Applications of Derivatives
CSCA Exam Prep
This formula is aligned to the CSCA undergraduate admissions exam syllabus. Continue with the linked tutorial and topic practice.
Practice related questions (8) · Start mock exam · Sign up — AI explanations · Membership plans
CSCA Mathematics Formula Reference
Formula and explanation
If the function f(x) is differentiable at x₀ and has a local extremum (maximum or minimum) at x₀, then f'(x₀) = 0. Note: Points where the derivative is zero are called stationary or critical points, but a stationary point is not necessarily an extremum (e.g., f(x) = x³ at x = 0 ).
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…
Plan your next CSCA study step
Use this topic in a focused practice set, then connect it to the exam requirements and timed papers.