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

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Systematic Curve Sketching with the Derivative
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Which step should always be completed first in systematic curve sketching?

Determining the domain

A function is even if it satisfies which condition?

f(x)=f(x)f(-x) = f(x)

What does f(x)>0f'(x) > 0 indicate about the function?

The function is increasing

Stationary points occur where which condition is satisfied?

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

What does f(x)>0f''(x) > 0 indicate about the curve?

Concave up

An inflection point occurs when which feature changes?

Concavity

Vertical asymptotes occur at discontinuities where the function approaches what?

Infinity

What gradient pattern indicates a maximum turning point?

Positive to zero to negative

Points where f(x)f'(x) is undefined are classified as what?

Not stationary points

A function is odd if it satisfies which condition?

f(x)=f(x)f(-x) = -f(x)

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