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Both calculators run independently — change the inputs on either side to compare results.

Concavity Calculator

Evaluates the second derivative of a cubic f(x) = ax³ + bx² + cx at a test point to determine concavity. Use it to classify intervals as concave up or concave down and locate inflection points.

Coefficient of x³

Coefficient of x²

Test Point x-value

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Calculus

Riemann Sum Calculator

Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums. Use this to understand numerical integration and error in calculus courses.

Function Coefficient

Power of x

Lower Bound

Upper Bound

Number of Subintervals

Riemann Sum Method

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Key differences

	Concavity Calculator	Riemann Sum Calculator
Category	Calculus	Calculus
Inputs required	3	6
Result	Second Derivative Value	Riemann Sum Approximation
What it does	Evaluates the second derivative of a cubic f(x) = ax³ + bx² + cx at a test point to determine concavity. Use it to classify intervals as concave up or concave down and locate inflection points.	Approximate the definite integral of a power function f(x) = c·xⁿ over an interval using left, right, or midpoint Riemann sums. Use this to understand numerical integration and error in calculus courses.