# finding optimal solution $w$ and classification accuracy

Suppose you are given $$6$$ one-dimensional points: $$3$$ with negative labels $$x_1 = −1$$, $$x_2 = 0$$, $$x_3 = 1$$ and $$3$$ with positive labels $$x_4 = −3$$, $$x_5 = −2$$, $$x_6 = 3$$. In this question, we first compare the performance of linear classifier with or without kernel. Then we solve for the maximum margin classifier using SVM.

Consider a linear classifier of form $$f(x) = sign(w_1x+w_0)$$. Write down the optimal value of $$w$$ and its classification accuracy on the above 6 points. There might be more than one optimal solution, writing down one of them is enough.

My attempt:
I understand that the data isn't linearly separable and that there will be some error, but I don't get how to get the optimal value of $$w$$. Do I minimize $$f(x)$$? But how do I take the derivative of $$f(x)$$? Any guidance would be appreciated, I'm a little lost.

The best that we can do is to classify $$5$$ points correctly and sacrifice one point.
We want to classify $$-1,0,1$$ as negative and $$-3,-2$$ as positivie. (we have to sacrifice $$3$$).
The boundary with maximum margin would be in the middle of $$-2$$ and $$-1$$. That is $$-\frac32$$.
$$sign(-(2x+3))=sign(-2x-3).$$