Hello,
In this question for answer d), I agree that it is easy to see that the sum of convex functions is convex. But do you have a trick to rapidly see that the minimum will indeed be in -10, 10? It's not obvious to me :)
So this is not very rigorous, but what I did was think of what a graph of x^4 will look like. Then imagine adding e^x(ignore the three) to all the values and subtract -3x from all the values. [-10,10] seemed wide enough and that the minumum would not have shifted more than 10 from zero from original x^4
Pb 4 exam 2016
Hello,
In this question for answer d), I agree that it is easy to see that the sum of convex functions is convex. But do you have a trick to rapidly see that the minimum will indeed be in -10, 10? It's not obvious to me :)
If you differentiate (d) and set the derivative equal to zero, you'll find that \(x=0\) is the unique minimizer.
1
So this is not very rigorous, but what I did was think of what a graph of x^4 will look like. Then imagine adding e^x(ignore the three) to all the values and subtract -3x from all the values. [-10,10] seemed wide enough and that the minumum would not have shifted more than 10 from zero from original x^4
1
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