The graph of the function g(x) is shown - HSC - SSCE Mathematics Advanced - Question 11 - 2024 - Paper 1
Question 11
The graph of the function g(x) is shown.
Using the graph, complete the table with the words positive, zero or negative as appropriate.
x-value First derivative ... show full transcript
Worked Solution & Example Answer:The graph of the function g(x) is shown - HSC - SSCE Mathematics Advanced - Question 11 - 2024 - Paper 1
Step 1
x-value = -3
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Answer
At x = -3, the graph is increasing, so the first derivative g'(x) is positive. The second derivative g''(x) is negative since the graph is concave down at this point.
Step 2
x-value = 1
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Answer
At x = 1, the graph has a local maximum, implying that the first derivative g'(x) is zero. The second derivative g''(x) is also zero, indicating a potential change in concavity.
Step 3
x-value = 5
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Answer
At x = 5, the graph is increasing, so the first derivative g'(x) is positive. The second derivative g''(x) is positive as well since the graph is concave up at this point.
