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Critical Points Calculator

Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.

x² Coefficient (a)

x Coefficient (b)

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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

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Key differences

	Critical Points Calculator	Trapezoidal Rule Calculator
Category	Calculus	Calculus
Inputs required	2	4
Result	Critical Point x-value	Approximate Integral
What it does	Finds the x-coordinate of the critical point (vertex) of a quadratic function ax² + bx + c by setting its derivative equal to zero. Use it to locate the maximum or minimum of any parabola instantly.	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.