Last updated on Sep 20, 2026

The Second Derivative (VCE SSCE Mathematical Methods): Quizzes

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The Second Derivative

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What is the second derivative?

Derivative of the derivative

In function notation, what symbol indicates the second derivative?

$f''(x)$ with double prime

If $f(x) = 2x^2 + 4x + 1$ , what is $f''(x)$ ?

$4$

What does the Leibniz notation $\frac{d^2y}{dx^2}$ emphasize?

Derivative twice with respect to $x$

What does the second derivative tell us about?

Curvature or concavity

If $f'(x) = 9x^2 - 2x^{-2}$ , what is $f''(x)$ ?

$18x + 4x^{-3}$

In motion, what does the second derivative of position $\frac{d^2x}{dt^2}$ give?

Acceleration

What does the first derivative of position $\frac{dx}{dt}$ give?

Velocity

If $f'(x) = 4x^3 - \frac{3}{2}x^{-\frac{5}{2}}$ , what is $f''(x)$ ?

$12x^2 + \frac{15}{4}x^{-\frac{7}{2}}$

How are $f''(x)$ and $\frac{d^2y}{dx^2}$ related?

Same mathematical operation

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