Second Derivative (Leaving Cert Mathematics): Flashcards

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Second Derivative
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What does the second derivative measure?

How the rate of change itself is changing

What does the first derivative tell you?

The slope (how fast yy changes with xx)

What does the second derivative tell about the slope?

How the slope is changing (curvature)

How is the second derivative obtained?

Derivative of the first derivative

Notation for second derivative of f(x)f(x)

f′′(x)f''(x)

f′(x)f'(x) for f(x)=2x2−4x+15f(x)=2x^2-4x+15

4x−44x-4

f′′(x)f''(x) for f(x)=2x2−4x+15f(x)=2x^2-4x+15

44

What term describes what the second derivative measures?

Curvature of the graph

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