Derivative & integral explorer
Build a polynomial and find its derivative and tangent line at a point — or its definite integral, compared against a Riemann sum you control.
Result
f(x) = x³ − 3x
f'(x) = 3x² − 3
f is flat (a critical point) at x = 1, and concave up.
Tangent line: y = -2 + 0(x − 1)
Dashed: tangent line at the marked point
How is this calculated?
The power rulesays d/dx[c·xⁿ] = n·c·xⁿ⁻¹ — apply it term by term and you get f'(x). f'(a) is the slope of the line tangent to the curve at x = a: positive means f is rising there, negative means falling, zero means a flat spot (a candidate for a local max or min). The second derivative, f''(a), tells you which way the curve bends — positive curves upward like a cup, negative curves downward like a dome.
New to the math? Learn the concept: Calculus, made visual