Mathematical formulas

Differential Calculus

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1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Criteria on closed intervals
Formula

9.2. Criteria on closed intervals

Formula

In 9.2. Criteria on closed intervals

Formula

V=\pi r^2h,\quad S=2\pi r^2+2\pi rh=C \Rightarrow V(r)=\frac{C}{2}r-\pi r^3

Tags

Differential calculus
Derivative
Optimization
Criteria on closed intervals

Detail

Typical example: cylinder with fixed surface area and maximum volume.

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Variables

$h$ Increment in the derivative definition
$S=2\pi r^2+2\pi rh=C \Rightarrow V(r)=\frac{C}{2}r-\pi r^3$ Pi constant

Conditions

$S=2\pi r^2+2\pi rh=C \Rightarrow V(r)=\frac{C}{2}r-\pi r^3$

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