Systematic Curve Sketching with the Derivative (HSC SSCE Mathematics Advanced): Flashcards

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Systematic Curve Sketching with the Derivative
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Even function definition

f(x)=f(x)f(-x) = f(x) for all xx in domain

Odd function definition

f(x)=f(x)f(-x) = -f(x) for all xx in domain

Where stationary points occur

Where f(x)=0f'(x) = 0

When a function is increasing

When f(x)>0f'(x) > 0

When a function is decreasing

When f(x)<0f'(x) < 0

When a curve is concave up

When f(x)>0f''(x) > 0

When a curve is concave down

When f(x)<0f''(x) < 0

When an inflection point occurs

Where concavity changes (f(x)f''(x) changes sign)

Gradient change for maximum turning point

Positive to zero to negative

First step in systematic curve sketching

Domain

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