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VCE 12 Methods 2023

6.03 Apply calculus to graphs

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

U34.AoS3.1

deducing the graph of the derivative function from the graph of a given function and deducing the graph of an anti-derivative function from the graph of a given function

U34.AoS3.11

features which link the graph of a function to the graph of the corresponding gradient function or its numerical values, the tangent to a curve at a given point and how the sign and magnitude of the derivative of a function can be used to describe key features of the function and its derivative function

U34.AoS3.15

evaluate derivatives of basic, transformed and combined functions and apply differentiation to curve sketching and related optimisation problems

U34.AoS3.4

application of differentiation to graph sketching and identification of key features of graphs, including stationary points and points of inflection, and intervals over which a function is strictly increasing or strictly decreasing

U34.AoS3.18

find derivatives of basic and more complicated functions and apply differentiation to curve sketching and optimisation problems

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