Summary (Grade 12 NSC Matric Mathematics): Quizzes

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What does a limit describe in relation to a function?

What f(x) approaches as x nears a value

What is the formula for average gradient?

f(x+h)−f(x)h\frac{f(x + h) - f(x)}{h}

What does the gradient at a point represent?

Slope of tangent line at that point

Which notation is most commonly used for derivatives?

f′(x)f'(x)

Using the power rule, what is ddx[x5]\frac{d}{dx}[x^5]?

5x45x^4

What is the derivative of any constant kk?

00

What is ddx[3f(x)]\frac{d}{dx}[3f(x)] equal to?

3⋅ddx[f(x)]3 \cdot \frac{d}{dx}[f(x)]

What does the second derivative measure?

How the rate of change is changing

When do stationary points occur?

Where f′(x)=0f'(x) = 0

In optimisation, what is done after differentiating the expression?

Set derivative equal to zero

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