For , let . If is a local minimum of and is the global minimum value, then is ________ (in integer).
For , let . If is a local minimum of and is the global minimum value, then is ________ (in integer).
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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).
Also written as: For k in R, let f(x)=x^4+2x^3+kx^2-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).
Single-variable optimisation has come up 37 times in 6 exams since 2010.
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.
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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.