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iGCSE (2021 Edition)

11.08 Using the first derivative

Interactive practice questions

Which of the following describes a maximum turning point?

A point where the tangent crosses the curve and the concavity changes from upwards to downwards or from downwards to upwards around the point.

A

A point where the tangent is horizontal and the concavity changes from upwards to downwards or from downwards to upwards around the point.

B

A point where the curve changes from decreasing to increasing.

C

A point where the curve changes from increasing to decreasing.

D
Easy
< 1min

Which of the following describes a minimum turning point?

Easy
< 1min

Consider the parabola with equation $y=x^2-4x+6$y=x24x+6.

Easy
4min

Consider the parabola with equation $y=5+x-x^2$y=5+xx2.

Easy
3min
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Outcomes

0606C14.2

Use the notations f'(x), f''(x), dy/dx, d^2y/dx^2 [=d/dx(dy/dx)].

0606C14.5B

Apply differentiation to stationary points.

0606C14.6

Use the first and second derivative tests to discriminate between maxima and minima.

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