Absolute Maximum and Minimum Values (VCE SSCE Mathematical Methods): Quizzes

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Absolute Maximum and Minimum Values
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What is the absolute maximum of a function on an interval?

The highest value anywhere on the domain

What is the absolute minimum of a function on an interval?

The lowest value anywhere on the domain

Where can absolute extrema occur?

Stationary points or endpoints

For f(x)=x2+2f(x) = x^2 + 2 on [−2,4][-2, 4], where does the absolute maximum occur?

At endpoint x=4x = 4

For f(x)=x3+2f(x) = x^3 + 2 on [−2,1][-2, 1], where do both extrema occur?

Both at endpoints

For a box with height xx and base (2−2x)(2-2x), what is the volume formula?

V=4x3−8x2+4xV = 4x^3 - 8x^2 + 4x

For V(x)=4x3−8x2+4xV(x) = 4x^3 - 8x^2 + 4x, what value of xx gives maximum volume (on [0,1][0,1])?

x=13x = \frac{1}{3}

If V(x)=4x3−8x2+4xV(x) = 4x^3 - 8x^2 + 4x with x≤0.3x \leq 0.3, where is the maximum?

At endpoint x=0.3x = 0.3

To find absolute extrema on [a,b][a,b], what values should you test?

All critical points and both endpoints

What should you always check when finding absolute extrema?

Both stationary points and endpoints

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Tangents and Normals

Rates of Change

Stationary Points

Absolute Maximum and Minimum Values

Maximum and Minimum Problems

Families of Functions

Applications to Motion in a Straight Line

Newton’s Method for Finding Solutions to Equations

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Tangents and Normals

Rates of Change

Stationary Points

Absolute Maximum and Minimum Values

Maximum and Minimum Problems

Families of Functions

Applications to Motion in a Straight Line

Newton’s Method for Finding Solutions to Equations

Explore VCE SSCE Mathematical Methods Flashcards by Topics

Tangents and Normals

Rates of Change

Stationary Points

Absolute Maximum and Minimum Values

Maximum and Minimum Problems

Families of Functions

Applications to Motion in a Straight Line

Newton’s Method for Finding Solutions to Equations

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Tangents and Normals

Rates of Change

Stationary Points

Absolute Maximum and Minimum Values

Maximum and Minimum Problems

Families of Functions

Applications to Motion in a Straight Line

Newton’s Method for Finding Solutions to Equations

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