Unit · year 1
MU-102 · Calculus I
Threads change7 theorems
The derivative and the integral, and the theorem that binds them into one subject.
Theorems in this unit
T-008
The chain rule
The derivative of a composition is the product of the derivatives.
T-009
Rolle's theorem
A differentiable function equal at two points has a stationary point between them.
T-010
The mean value theorem
A differentiable function attains its average rate of change at some interior point.
T-011
The extreme value theorem
A continuous function on a closed interval attains a maximum and a minimum.
T-012
The fundamental theorem of calculus
Differentiation and integration are inverse operations.
T-013
Taylor's theorem with remainder
A smooth function equals its Taylor polynomial plus a controllable error term.
T-014
L'Hôpital's rule
Indeterminate limits of ratios can be resolved by differentiating numerator and denominator.