Last updated on Oct 23, 2026

Further Applications of Differentiation (HSC SSCE Mathematics Advanced): Quizzes

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Further Applications of Differentiation

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What is $\frac{d}{dx}(\log_e x)$ ?

$\frac{1}{x}$

What is the gradient of the tangent to $y = \log_e x$ at $(e, 1)$ ?

$\frac{1}{e}$

If a tangent has gradient $\frac{1}{e}$ , what is the gradient of the normal?

$-e$

What is the domain of $y = x \log_e x$ ?

$x > 0$

Where does $y = x \log_e x$ cross the x-axis?

$x = 1$

What is $\frac{dy}{dx}$ for $y = x \log_e x$ ?

$\log_e x + 1$

Where is the stationary point of $y = x \log_e x$ ?

$x = e^{-1}$

What is the nature of the stationary point at $x = e^{-1}$ for $y = x \log_e x$ ?

Minimum

What can be said about concavity of $y = x \log_e x$ for $x > 0$ ?

Always concave up

What is $\lim_{x \to 0^+} x \log_e x$ ?

$0$

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Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Sequences and Series

Graphs and Equations

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Motion and Rates

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Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

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Motion and Rates

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