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Determining extrema

Task number: 3046

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Variant 1
the maximum values of the function \(x^{1/x}\) over its domain of definition.

Difficulty level: Easy task (using definitions and simple reasoning)

Routine calculation training

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Review (27)
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Suprema and infima, properties of reals (6)
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- infimum of set of real numbers bounded below (L1)
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Sequences and limits of sequences (16)
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Simple series (5)
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Convergence and absolute convergence I (12)
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Limits of functions (15)
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Derivatives (10)
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- Applications of derivatives: extreme values (L1)
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Limits of functions II (4)
- Limits of ratios (L1)
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The shape of functions (8)
- Determining extrema (L1)
- Extrema (L2)
- Shape of a function (without convexity) (L1)
- Shape of a function (with convexity) (L1)
- Application - word problems (L1)
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Convergence and absolute convergence II (1)
- Series with a parameter in the exponent (L1)
Polynomials, partial fraction decomposition (3)
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Taylor polynomials (4)
Indefinite integrals (12)
- Table - basic integrals (L1)
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The definite integral and its applications (6)
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Metric spaces (11)
Functions of several variables (9)
- Limits (L1)
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- Domain, continuity, boundedness of functions (L1)
- Partial derivatives (L1)
- Equivalence of partial derivatives (L1)
- Extrema (L1)
- The total differential (L1)
- A function without a total differential (L1)
- The total differential for composite function (L2)
Implicit functions (5)
- Derivative of a simple function (L1)
- Partial derivative of an implicit function (L1)
- Astroids (L1)
- An implicit function of two variables (L2)
- An increasing implicit function (L1)
Bounded extrema (1)
- Bounded extrema (L1)

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Updated: Jun. 23rd, 2020