Find a local minimum and a local maximum of the function .
Tap an option to check your answer.
0 marksMathematicsSingle-variable optimisationUnconstrained extrema and the first- and second-order conditionsModerateabout 2 min
JNU SIS 2020 Question 43: Single-variable optimisation
Answer and worked solution
Checking your account…
Plain-text version
f(x) = x⁴ - 4x³ + 4x² + 4 Find a local minimum and a local maximum of the function f(x). (A) 1, 2 (B) 3, 4 (C) 2, 1 (D) None of the above
Also written as: f(x) = x^4 - 4x^3 + 4x^2 + 4 Find a local minimum and a local maximum of the function f(x).
Single-variable optimisation has come up 37 times in 6 exams since 2010.
What this question tests
This question is on Unconstrained extrema and the first- and second-order conditions, part of Single-variable optimisation in Mathematics.
Finding and classifying maxima and minima using derivatives.
TestStop has 12 past-paper questions on this subtopic.
Similar questions from other papers
- A company has determined that total cost C, total revenue R and the number of units produced X are related as C = 100 + 0.015 X^2 and R = 3X. Find the product level X…
- For k∈ℝ, let f(x)=x⁴+2x³+kx²-k. If x=3/2 is a local minimum of f and m is the global minimum value, then f(0)-m is (in integer).
- Suppose f(.) is a continuous function over a closed and bounded interval [a, b]. Then there exists a point d in [a, b] where f(.) has a minimum, and a point c in [a, b]…
- Let f(x) = x², and the domain of x is [1, 2]. Which of the following statements is true?
- If the demand function for the product of a firm is p = √(1350 - 6q), find the output level that maximizes total revenue.
Question from the JNU SIS 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.