Stationary Points & Turning Points (AQA A-Level Mathematics): Quizzes

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Stationary Points & Turning Points
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A stationary point occurs where which condition is met?

f′(x)=0f'(x) = 0

If f′′(x)>0f''(x) > 0 at a stationary point, what type is it?

Local minimum

If f′′(x)<0f''(x) < 0 at a stationary point, what type is it?

Local maximum

What does f′′(x)=0f''(x) = 0 at a stationary point indicate?

Test is inconclusive

If f′(x)f'(x) changes from positive to negative, what is the stationary point?

Local maximum

Which statement about turning points is correct?

All turning points are stationary

What indicates a point of inflection when f′′(x)=0f''(x) = 0?

f′(x)f'(x) same sign both sides

If f′(x)f'(x) changes from negative to positive, what is the point?

Local minimum

For y=x3−12xy = x^3 - 12x, what are the xx-values of stationary points?

x=±2x = \pm 2

For y=x3−12xy = x^3 - 12x, if d2ydx2=6x\frac{d^2y}{dx^2} = 6x, classify the point at x=2x = 2.

Minimum

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Differentiation

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Further Applications of Differentiation

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Differentiation

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Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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Differentiation

Applications of Differentiation

Further Differentiation

Further Applications of Differentiation

Implicit Differentiation

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