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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

Rectangular Rule Integration

Approximate a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.

Lower Bound (a)

Upper Bound (b)

Number of Intervals (n)

Average Function Value

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Key differences

	Critical Points Calculator	Rectangular Rule Integration
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 a definite integral using a rectangular (midpoint-style) rule with a chosen number of subintervals and an averaged function value. Returns the area of a single representative rectangle of width Δx.