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Glossary

Look up any term from this course. Each entry links back to the lesson that taught it.

Glossary of course terms
Term	Definition	Lesson
Antiderivative	$A function F(x) with F'(x) = f(x) — reversing differentiation. Always includes + C.$	Antiderivatives
Constant multiple rule	$A number multiplying a function stays in place while its rest is differentiated: (k \cdotf)' = k \cdotf'.$	Sum, Difference, and Constant Multiple Rules
Decreasing function	$A function is decreasing where f'(x) < 0 — its graph falls.$	Increasing and Decreasing Functions
Definite integral	$Written \int from a to b of f(x)dx, equal to F(b) - F(a) — gives the exact area under a curve between a and b.$	Definite Integrals and Area
Derivative	$The exact gradient of a curve at a point, f'(x), defined as the limit of the secant gradient as h \to 0 .$	The Derivative
Fundamental theorem of calculus	$The rule connecting differentiation and integration: area under f(x) from a to b equals F(b) - F(a).$	Definite Integrals and Area
Increasing function	$A function is increasing where f'(x) > 0 — its graph rises.$	Increasing and Decreasing Functions
Indefinite integral	$Written \intf(x)dx — another name for finding the antiderivative of f(x).$	Integration Rules
Limit	$The value an expression approaches as its input gets closer and closer to a target value.$	Limits
Maximum point	$A stationary point where f' changes from positive to negative — a peak.$	Stationary Points
Minimum point	$A stationary point where f' changes from negative to positive — a dip.$	Stationary Points
Power rule	$If f(x) = x^{n}, then f'(x) = n \cdot x^{n - 1} .$	The Power Rule
Rate of change	$How much one quantity changes compared to a change in another: (change in y) \div (change in x).$	Rate of Change
Secant line	$A straight line that crosses a curve at two points.$	The Gradient of a Curve
Stationary point	$A point where f'(x) = 0 — the tangent line there is horizontal.$	Stationary Points
Sum and difference rules	$Differentiate (or integrate) a sum or difference term by term.$	Sum, Difference, and Constant Multiple Rules
Tangent line	$A straight line that touches a curve at exactly one point, matching the curve's direction there.$	The Gradient of a Curve
Velocity	$The derivative of position with respect to time: v(t) = s'(t).$	Applications of Differentiation