Summary of Optimization on Open or Unbounded Intervals
Read this topicExplanations 2
- Optimization on open or unbounded intervals is almost exactly the same as optimization on closed intervals. Suppose that we have a function f(x)f(x)f(x) which we would like to o…
By Sujay Kazi, Victor Wang
- In other words, trivial inequality x2≥0x^2 \ge 0x2≥0 is trivial. That's it! Many times you can solve optimization problems just by thinking a bit, instead of mechanically using …
By Victor Wang, Victor Wang
Problems 5
- Karen is attempting to climb a rope that is not securely fastened. If she pulls herself up xxx feet at once, then the rope slips x3/3x^3/3x3/3 feet down. How many feet at a time…
- Find the absolute maximum of f(x)=12+4x−x2f(x) = 12 + 4x - x^2f(x)=12+4x−x2.
- Find the global minimum value of f(x)=xlnxf(x) = x \ln xf(x)=xlnx.
- What is the global maximum of the function f(x)=−3x4+6x2+5f(x) = -3x^4 + 6x^2 + 5f(x)=−3x4+6x2+5?
- Let aaa be a real constant, and define the integral function F(x)=∫ax(2t−2) dtF(x) = \int_a^x (2^t - 2)\,dtF(x)=∫ax(2t−2)dt. Suppose aaa is such that F(2016)=2017F(2016) = 2017…