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VCE 12 Methods 2023

6.04 The first derivative

Interactive practice questions

The gradient function of $g\left(x\right)$g(x) is $g'\left(x\right)=3$g(x)=3.

Select all possible graphs of $g\left(x\right)$g(x).

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A

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B

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C

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D
Easy
1min

Sketch the linear function that satisfies the following information

$f\left(0\right)=1$f(0)=1

$f'\left(2\right)=3$f(2)=3

Easy
1min

Consider the four functions sketched below.

Which of the sketches match the information for $f\left(x\right)$f(x) shown in the table? Select all the correct options.

Easy
1min

The gradient function, $f'\left(x\right)$f(x) is graphed below.

Select all possible graphs of $f\left(x\right)$f(x).

Easy
1min
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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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