Mock Midterm ECON 1530
ECON 1530
Mock Midterm
Chapters 8 to 9.3 (Single Variable Optimization)
Time: 90 minutes Total: 70 marks
Instructions:
• Answer all questions.
• Show all algebraic steps clearly.
• Use exact expressions before numerical approximation.
1
, Mock Midterm ECON 1530
Question 1 (10 marks)
Let f (x) = x3 − 6x2 + 9x + 1.
(a) Compute f ′ (x) and find all critical points. (3)
(b) Determine intervals where f is increasing/decreasing. (3)
(c) Compute f ′′ (x) and identify concavity and any inflection point. (4)
2
ECON 1530
Mock Midterm
Chapters 8 to 9.3 (Single Variable Optimization)
Time: 90 minutes Total: 70 marks
Instructions:
• Answer all questions.
• Show all algebraic steps clearly.
• Use exact expressions before numerical approximation.
1
, Mock Midterm ECON 1530
Question 1 (10 marks)
Let f (x) = x3 − 6x2 + 9x + 1.
(a) Compute f ′ (x) and find all critical points. (3)
(b) Determine intervals where f is increasing/decreasing. (3)
(c) Compute f ′′ (x) and identify concavity and any inflection point. (4)
2
