Last updated on Sep 20, 2026

When Is a Function Differentiable? (VCE SSCE Mathematical Methods): Flashcards

📚Flashcards

Revision Notes Model Answers Quizzes Flashcards Exam Questions

When is a function differentiable?

Practise the cards

10 cards from this deck

Show

Condition for differentiability at $x = a$

Limit $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ exists

What $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ represents

The derivative at $x = a$

Piecewise: smooth join → differentiable?

Yes

Piecewise: sharp corner → differentiable?

Is $|x|$ differentiable at $x = 0$ ?

Is $x^{\frac{1}{3}}$ differentiable at $x = 0$ ?

Differentiable → continuous?

Yes, always

Continuous → differentiable?

Not necessarily

Stronger condition: differentiability or continuity?

Differentiability

Check piecewise differentiability at boundary: verify what?

Derivatives from both sides are equal

Join 100,000+ SSCE students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.

When Is a Function Differentiable? (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Condition for differentiability at x=ax = ax=a

What lim⁡h→0f(a+h)−f(a)h\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}limh→0​hf(a+h)−f(a)​ represents

Piecewise: smooth join → differentiable?

Piecewise: sharp corner → differentiable?

Is ∣x∣|x|∣x∣ differentiable at x=0x = 0x=0?

Is x13x^{\frac{1}{3}}x31​ differentiable at x=0x = 0x=0?

Differentiable → continuous?

Continuous → differentiable?

Stronger condition: differentiability or continuity?

Check piecewise differentiability at boundary: verify what?

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

Condition for differentiability at $x = a$

What $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ represents

Is $|x|$ differentiable at $x = 0$ ?

Is $x^{\frac{1}{3}}$ differentiable at $x = 0$ ?