Last updated on Oct 23, 2026

Applications of Differentiation (HSC SSCE Mathematics Advanced): Flashcards

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Applications of Differentiation

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Point both $e^x$ & $e^{-x}$ pass through

$(0, 1)$

Type of change $y = e^x$ represents

Exponential growth

Type of change $y = e^{-x}$ represents

Exponential decay

Gradient of $y = e^x$ at $(0, 1)$

$1$

Gradient of $y = e^{-x}$ at $(0, 1)$

$-1$

$e^x$ and $e^{-x}$ graph relationship

Reflections in $y$ -axis

$\lim_{x \to \infty} xe^{-x}$

$0$ (exponential dominates)

Transformation: replacing $x$ with $-x$

Reflection in $y$ -axis

Examples of exponential decay

Radioactive decay, cooling, sound decay, capacitor discharge

Exponential vs polynomial in limits

Exponential dominates polynomial

Explore HSC SSCE Mathematics Advanced Revision Notes by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

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Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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