Complete Theory

Worked Examples

Example 1Complete analysis of

f(x)=xe^{-x}

Example 2Complete analysis of

f(x)=\dfrac{x^2}{x^2-1}

Exercise 1Function analysis — cubic polynomialMedium

📋 Problem to solve

Fully analyze

f(x)=x^3-3x

and find maxima, minima, inflection points.

Exercise 2Function analysis — rational functionHard

📋 Problem to solve

Fully analyze

f(x)=\dfrac{x-1}{x+1}

Exercise 3Function analysis — logarithmHard

📋 Problem to solve

Fully analyze

f(x)=x-\ln x

Exercise 4Function analysis — oblique asymptoteVery Hard

📋 Problem to solve

Fully analyze

f(x)=xe^{1/x}

📚

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