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Year 12 · Calculus

Stationary points

A stationary point is where the gradient is zero: a maximum, minimum or point of inflection.

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How to do it

  1. Differentiate and set the derivative to zero.
  2. Solve for x.
  3. Second derivative positive: minimum. Negative: maximum.

Worked example

At what value of x is the stationary point of y = -x² + 2x − 1?
dy/dx = -2x + 2 = 0 gives x = 1. (Or use x = −b/2a.)
Answer: 1

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Set the derivative, not the function, to zero.

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