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4.02 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 function $f\left(x\right)=-2\left(x+2\right)^2+4$f(x)=2(x+2)2+4 drawn below.

Easy
2min

Consider the function $f\left(x\right)=-\left(x-4\right)^3+7$f(x)=(x4)3+7 drawn below.

Easy
1min
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Outcomes

MA12-3

applies calculus techniques to model and solve problems

MA12-6

applies appropriate differentiation methods to solve problems

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