The Second Derivative (VCE SSCE Mathematical Methods): Flashcards

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The Second Derivative
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Second derivative definition

The derivative of the derivative

What second derivative tells about rate of change

How the rate of change itself is changing

Second derivative info about function shape

Curvature or concavity of the function

Function notation for second derivative

f(x)f''(x)

Leibniz notation for second derivative

d2ydx2\frac{d^2y}{dx^2}

First derivative of position x(t)x(t)

Velocity dxdt\frac{dx}{dt}

Second derivative of position x(t)x(t)

Acceleration d2xdt2\frac{d^2x}{dt^2}

What velocity tells us

How quickly position is changing

What acceleration tells us

How quickly velocity is changing

Process to find second derivative

Apply the power rule twice

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