Curve-Sketching Using the Derivative (HSC SSCE Mathematics Advanced): Quizzes

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Increasing, Decreasing, and Stationary at a Point
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If f′(a)>0f'(a) > 0, what is the behavior of f(x)f(x) at x=ax = a?

f(x)f(x) is increasing

What condition must be satisfied for f(x)f(x) to be stationary at x=ax = a?

f′(a)=0f'(a) = 0

If f′(a)<0f'(a) < 0, how does yy change as xx increases at that point?

yy decreases

For f(x)=x3−12xf(x) = x^3 - 12x, given f′(x)=3x2−12f'(x) = 3x^2 - 12, what is the behavior at x=5x = 5?

Increasing

To find where a curve is stationary, what equation must be solved?

f′(x)=0f'(x) = 0

For y′=2(x−3)y' = 2(x - 3), for what values of xx is the curve decreasing?

x<3x < 3

If f′(x)=3x2+1f'(x) = 3x^2 + 1, what can be said about f(x)f(x)?

Always increasing

What does a horizontal tangent indicate about a curve at that point?

The curve is stationary

For y=x4−4xy = x^4 - 4x with y′=4(x3−1)y' = 4(x^3 - 1), at what value of xx is the curve stationary?

x=1x = 1

What does the sign of f′(a)f'(a) tell us about the curve at x=ax = a?

The behavior of the curve

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Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

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The Trigonometric Functions

Motion and Rates

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Displaying and Interpreting Data

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Explore HSC SSCE Mathematics Advanced Flashcards by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

Explore HSC SSCE Mathematics Advanced Exam Questions by Topics

Sequences and Series

Graphs and Equations

Curve-Sketching Using the Derivative

Integration

The Exponential and Logarithmic Functions

The Trigonometric Functions

Motion and Rates

Series and Finance

Displaying and Interpreting Data

Continuous Probability Distributions

Show more

Displaying and Interpreting Data

Continuous Probability Distributions

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