Finding Extrema Using Derivatives (First Derivative Test)
If a function f(x) is differentiable at point x₀ and attains an extremum at x₀, then f'(x₀) = 0 (Fermat's Theorem). General steps to find extrema of f(x): 1. F…
Syllabus path: Functions › Concepts and Properties of Functions › Maximum and Minimum Values of a Function
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 (12) · Start mock exam · Sign up — AI explanations · Membership plans
CSCA Mathematics Formula Reference
Formula and explanation
If a function f(x) is differentiable at point x₀ and attains an extremum at x₀, then f'(x₀) = 0 (Fermat's Theorem). General steps to find extrema of f(x): 1. Find the domain. 2. Find the derivative f'(x). 3. Set f'(x) = 0 to find critical points (stationary points). 4. Check the sign change of f'(x) around the critical point: positive to negative indicates a local maximum; negative to positive indicates a local minimum. Applicable Condition: The function is differentiable on the relevant interval.
Related tutorial and examples
Maximum and Minimum Values of a Function
Maximum and Minimum Values of a Function 1. Concept The Maximum and Minimum Values (collectively called Global Extrema) describe the boundaries of the function's output range over its entire domain or a specific interval. Let the domain of y = f(x) be D: Maximum Value: If there e…
Plan your next CSCA study step
Use this topic in a focused practice set, then connect it to the exam requirements and timed papers.