Second Order Derivatives (Edexcel A-Level Mathematics): Quizzes

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Second Order Derivatives
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What does the second derivative f′′(x)f''(x) represent?

Rate of change of the first derivative

If f′′(x)>0f''(x) > 0 for all xx in an interval, what is the shape of the graph?

Concave up (U-shaped)

If f′′(x)<0f''(x) < 0 for all xx in an interval, what is the shape of the graph?

Concave down (inverted U-shaped)

What is an inflection point?

A point where concavity changes

For f(x)=x3−3x2+2xf(x) = x^3 - 3x^2 + 2x, what is f′′(x)f''(x)?

6x−66x - 6

At a critical point x=cx = c, if f′′(c)>0f''(c) > 0, what is f(c)f(c)?

A local minimum

At a critical point x=cx = c, if f′′(c)<0f''(c) < 0, what is f(c)f(c)?

A local maximum

If d2ydx2>0\frac{d^2y}{dx^2} > 0, what is happening to the gradient?

The gradient is increasing

In physics, what does the second derivative of position with respect to time give?

Acceleration

At a critical point, if f′′(c)=0f''(c) = 0, what can we conclude?

The test is inconclusive

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Differentiation

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Further Applications of Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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