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Use a derivative to analyse and recognise the graph of a function

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
stationary-points:cubic:two-simple:all:maximum:datastationary-points:cubic:two-simple:all:minimum:dataNOWMix of allRecommended
Question 1 of 8

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Use the displayed function rule

Calculate the stationary points from the derivative

\[g(t)=-\frac{1}{9}\,t^{3} + \frac{1}{6}\,t^{2} - \frac{1}{18}\]

The domain is all real values of \(t\)

(a)5 marks

Complete the derivative-sign table. Enter -1 for a negative derivative, 0 for zero and 1 for a positive derivative

Derivative sign table
\(t\)sign of g'(t)
\(-1\)\(?\)
\(0\)\(?\)
\(\frac{1}{2}\)\(?\)
\(1\)\(?\)
\(2\)\(?\)
(b)5 marks

Complete the exact feature table with the y-intercept and stationary coordinates

Function features
FeatureValue
y-intercept ordinate\(?\)
stationary input 1\(?\)
stationary ordinate 1\(?\)
stationary input 2\(?\)
stationary ordinate 2\(?\)
(c)1 mark

Classify the stationary point at \(t=1\)