Last updated on Sep 20, 2026

The Derivative (VCE SSCE Mathematical Methods): Quizzes

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The Derivative

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What formula gives the average rate of change of $f(x)$ over interval $[a, b]$ ?

$\frac{f(b) - f(a)}{b - a}$

What is a tangent to a curve?

A line touching the curve at exactly 1 pt

What is the formal definition of the derivative $f'(x)$ ?

$\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

What is the derivative of $x^2$ ?

$2x$

Evaluate $\lim_{h \to 0} (22x^2 + 20xh + h)$

$22x^2$

A chord is defined as:

A line segment joining 2 pts on a curve

If $f(x) = 3x^2 + 2x + 2$ , what is $f'(x)$ by first principles?

$6x + 2$

What is the central difference approximation for $f'(a)$ ?

$\frac{f(a+h) - f(a-h)}{2h}$

How does instantaneous rate differ from average rate?

It's the rate at a specific pt, not interval

For $f(x) = x^3$ at pt $(2, 8)$ , what is the tangent gradient?

$12$

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