Second Derivative (Grade 12 NSC Matric Mathematics): Quizzes

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Second Derivative
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What does the second derivative measure?

Rate of change of the gradient

Which notation represents the second derivative?

f′′(x)f''(x)

How many times must you differentiate to find the second derivative?

Twice

Find k′′(x)k''(x) if k(x)=2x3−4x2+9k(x) = 2x^3 - 4x^2 + 9

12x−812x - 8

What is d2ydx2\frac{d^2y}{dx^2} for y=3xy = \frac{3}{x}?

6x3\frac{6}{x^3}

Find f′′(x)f''(x) for f(x)=5x2+3x−7f(x) = 5x^2 + 3x - 7

1010

What is a common mistake when finding the second derivative?

Squaring the first derivative

Before differentiating 3x\frac{3}{x}, how should you rewrite it?

3x−13x^{-1}

What does the second derivative reveal about a function?

Curvature and concavity

How is d2ydx2\frac{d^2y}{dx^2} read aloud?

d squared y, d x squared

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