Families of Functions (VCE SSCE Mathematical Methods): Quizzes

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Families of functions
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What is a family of functions?

Functions with same form, diff parameters

For f(x)=(x−a)2(x−b)f(x) = (x - a)^2(x - b), what is f′(x)f'(x)?

f′(x)=(x−a)(3x−a−2b)f'(x) = (x - a)(3x - a - 2b)

Where do stationary points occur?

Where f′(x)=0f'(x) = 0

For f(x)=(x−a)2(x−b)f(x) = (x - a)^2(x - b), the second stationary point is at x=x = ?

x=a+2b3x = \frac{a + 2b}{3}

For f(x)=(x−a)2(x−b)f(x) = (x - a)^2(x - b), what is the nature of the point (a,0)(a, 0)?

Always a local maximum

For f′(x)=(x−a)(3x−a−2b)f'(x) = (x - a)(3x - a - 2b), what is the sign when x<ax < a?

f′(x)>0f'(x) > 0 (positive)

If y=x3−3x2y = x^3 - 3x^2 has turning points at (0,0)(0, 0) and (2,−4)(2, -4), what are they after translation?

(a,b)(a, b) and (2+a,−4+b)(2 + a, -4 + b)

For y=x3−3x2y = x^3 - 3x^2, what are the turning points?

(0,0)(0, 0) and (2,−4)(2, -4)

How many pieces of info does a stationary point give?

Two: point on curve and f′(x)=0f'(x) = 0

For f(x)=ax3+bx2+cxf(x) = ax^3 + bx^2 + cx with stationary point (1,6)(1, 6), express aa in terms of cc.

a=c−12a = c - 12

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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