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

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Stationary Points & Turning Points
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At what condition does a stationary point occur on the graph of f(x)f(x)?

When f′(x)=0f'(x) = 0

What is true about turning points and stationary points?

All turning points are stationary points

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

Local minimum

If f′′(x)<0f''(x) < 0 at a stationary point, what does this indicate?

Local maximum

How does the graph behave at a local maximum turning point?

Changes from increasing to decreasing

How does the graph behave at a local minimum turning point?

Changes from decreasing to increasing

What should you do if f′′(x)=0f''(x) = 0 at a stationary point?

Test gradient left and right of point

If f′(x)f'(x) doesn't change sign at a stationary point, what is it?

Saddle point (not a turning point)

What indicates a point of inflection when testing gradients?

Same sign both sides (+ to + or - to -)

What is the first step in finding stationary points of f(x)f(x)?

Find the first derivative f′(x)f'(x)

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