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3.04 Graphing techniques using calculus

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

Which of the following describes a horizontal point of inflection?

Easy
< 1min

Consider the function $f\left(x\right)=9x^2+18x-16$f(x)=9x2+18x16.

Easy
8min
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Outcomes

3.1.13

understand the concepts of concavity and points of inflection and their relationship with the second derivative

3.1.14

understand and use the second derivative test for determining local maxima and minima

3.1.15

sketch the graph of a function using first and second derivatives to locate stationary points and points of inflection

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