Rates of Change (VCE SSCE Mathematical Methods): Quizzes

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Rates of change
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What is the average rate of change of f(x)f(x) over interval [a,b][a, b]?

f(b)−f(a)b−a\frac{f(b) - f(a)}{b - a}

What gives the instantaneous rate of change of f(x)f(x) at x=ax = a?

f′(a)f'(a)

If dydx>0\frac{dy}{dx} > 0, what happens to yy as xx increases?

yy is increasing

If dydx<0\frac{dy}{dx} < 0, what happens to yy as xx increases?

yy is decreasing

What does average rate of change represent geometrically?

Gradient of secant line

For f(x)=x2+2xf(x) = x^2 + 2x, what is the average rate of change over [2,3][2, 3]?

77

For V=600−10t−1100t2V = 600 - 10t - \frac{1}{100}t^2, what is dVdt\frac{dV}{dt} when t=10t = 10?

−1015-10\frac{1}{5} cm³/s

For T=20+60e−0.3tT = 20 + 60e^{-0.3t}, what is dTdt\frac{dT}{dt} when T=80T = 80°C?

−18-18°C/min

In cooling, what is the rate of temperature change proportional to?

Temperature difference from room

Why check when V=0V = 0 for the balloon volume model?

Volume cannot be negative

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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