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Critical Points Calculator

Find and classify critical points of a cubic polynomial ax³ + bx² + cx + d. Use it when you need to locate local maxima, minima, and inflection points quickly.

Coefficient of x³

Coefficient of x²

Test Point x =

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Calculus

Trapezoidal Rule Calculator

Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.

Lower Limit (a)

Upper Limit (b)

Number of Subintervals

Average Trapezoid Height

Fill in the required fields to see your result.

Key differences

	Critical Points Calculator	Trapezoidal Rule Calculator
Category	Calculus	Calculus
Inputs required	3	4
Result	Second Derivative at Test Point	Approximate Integral
What it does	Find and classify critical points of a cubic polynomial ax³ + bx² + cx + d. Use it when you need to locate local maxima, minima, and inflection points quickly.	Approximate the definite integral of a function over [a, b] by summing trapezoid areas across n subintervals. Ideal for numerical integration when an antiderivative is difficult or impossible to find analytically.