Calculus
Critical Points Calculator
Find local maxima, minima, and saddle points. Determine the critical points of a function by finding where the first derivative is zero or undefined, and classify them using the first derivative test.
d/dx
Examples:
Differentiation Rules
Power Rule
d/dx [x^n] = nx^(n-1)
Product Rule
[fg]' = f'g + fg'
Chain Rule
d/dx [f(g(x))] = f'(g(x))g'(x)
Constant Rule
d/dx [c] = 0
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Solution Methodology
01
Find First Derivative
Compute f'(x) using differentiation rules.
02
Solve f'(x) = 0
Find the x-values that make the derivative zero or undefined.
03
Classify Extrema
Test intervals around the critical points to determine max, min, or saddle points.
Common Questions
What is a critical point?
A critical point of a function is a point on the graph where the first derivative is either zero (horizontal tangent) or undefined. These are the candidate points for local maximums and minimums.
How do you classify a critical point?
Use the First Derivative Test. If the derivative changes from positive to negative at the point, it is a local maximum. If it changes from negative to positive, it is a local minimum. If the sign doesn't change, it is neither.