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0580 · Notes & worked examples

Stationary points of a cubic · Short practice

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Recall

Stationary points of a cubic — objective 1

Maths4U Original · Short practice

\(f(x)=x^{3} - 3 x + 6\).

Find the smaller stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Stationary points of a cubic — objective 1

Maths4U Original · Short practice

\(f(x)=2 x^{3} - 24 x + 7\).

Find the smaller stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Method

Stationary points of a cubic — objective 2

Maths4U Original · Short practice

\(f(x)=2 x^{3} - 24 x + 7\).

Find the larger stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Stationary points of a cubic — objective 2

Maths4U Original · Short practice

\(f(x)=3 x^{3} - 81 x + 8\).

Find the larger stationary x-coordinate.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Apply

Stationary points of a cubic — objective 3

Maths4U Original · Short practice

\(f(x)=3 x^{3} - 81 x + 8\).

Find the local maximum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Stationary points of a cubic — objective 3

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 192 x + 9\).

Find the local maximum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Check understanding

Stationary points of a cubic — objective 4

Maths4U Original · Short practice

\(f(x)=4 x^{3} - 192 x + 9\).

Find the local minimum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Stationary points of a cubic — objective 4

Maths4U Original · Short practice

\(f(x)=x^{3} - 75 x + 2\).

Find the local minimum value.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Try written exam-style problems →