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

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Question 1 of 8

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The rule for a function is shown below

Obtain the stationary coordinates of the curve

\[q(z)=\frac{1}{6}\,z^{3} + \frac{3}{8}\,z^{2} + \frac{1}{4}\,z + \frac{1}{24}\]

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

(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
\(z\)sign of q'(z)
\(-2\)\(?\)
\(-1\)\(?\)
\(-\frac{3}{4}\)\(?\)
\(-\frac{1}{2}\)\(?\)
\(\frac{1}{2}\)\(?\)
(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 \(z=-1\)