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The Graph of the Derivative Function (VCE SSCE Mathematical Methods): Flashcards

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The Graph of the Derivative Function

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What does $f'(x)$ tell us?

Gradient/slope of $f(x)$ at every point

Derivative of quadratic function

Linear function (straight line)

Derivative of cubic function

Quadratic function (parabola)

How does degree change from $f(x)$ to $f'(x)$ ?

Degree drops by one

When $f'(x) > 0$ , what is $f(x)$ doing?

Increasing (going upward)

When $f'(x) < 0$ , what is $f(x)$ doing?

Decreasing (going downward)

At turning points, what is $f'(x)$ ?

Zero (derivative crosses $x$ -axis)

Derivative of linear function

Constant (horizontal line)

Where is $f(x) = |x|$ not differentiable?

At $x = 0$ (sharp corner)

What causes non-differentiability?

Sharp corners, cusps, vertical tangents, discontinuities

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The Graph of the Derivative Function (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

What does f′(x)f'(x)f′(x) tell us?

Derivative of quadratic function

Derivative of cubic function

How does degree change from f(x)f(x)f(x) to f′(x)f'(x)f′(x)?

When f′(x)>0f'(x) > 0f′(x)>0, what is f(x)f(x)f(x) doing?

When f′(x)<0f'(x) < 0f′(x)<0, what is f(x)f(x)f(x) doing?

At turning points, what is f′(x)f'(x)f′(x)?

Derivative of linear function

Where is f(x)=∣x∣f(x) = |x|f(x)=∣x∣ not differentiable?

What causes non-differentiability?

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Explore VCE SSCE Mathematical Methods Quizzes by Topics

Antidifferentiation of Polynomial Functions

The Second Derivative

Sketching Graphs

The Derivative

Rules for Differentiation

Differentiating Where n is a Negative Integer

The Graph of the Derivative Function

The Chain Rule

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

When Is a Function Differentiable?

Differentiating Rational Powers

Differentiation of Different Functions

Derivatives of Circular Functions

The Product Rule

The Quotient Rule

Limits and Continuity

What does $f'(x)$ tell us?

How does degree change from $f(x)$ to $f'(x)$ ?

When $f'(x) > 0$ , what is $f(x)$ doing?

When $f'(x) < 0$ , what is $f(x)$ doing?

At turning points, what is $f'(x)$ ?

Where is $f(x) = |x|$ not differentiable?