Function f(x):

Examples: `x^3 - 3*x`, `3*x^2 + 5*x - 2`, `sin(x) + x`

Evaluation Point x = a (Tangent Point):

Examples: `2`, `e`, `pi/2`, `1/3`

Derivative f'(x)

$$f'(x) = 0$$

Derivative $f'(x)$: Represents the slope of the tangent line at any point on the original function $f(x)$.
Tangent Line Equation: The tangent line equation at point $(a, f(a))$ on the curve is represented as $y - f(a) = m(x - a)$ where the slope is $m = f'(a)$.
Increase/Decrease Table: By analyzing the sign (positive or negative) of the derivative, this table shows whether the function is increasing ($f'(x) > 0 \rightarrow \nearrow$) or decreasing ($f'(x) < 0 \rightarrow \searrow$). Points where $f'(x) = 0$ are candidates for local maxima and local minima (extreme values).

Differentiation & Tangent Solver