How does cost function of logistic regression create a convex that the gradient decent can use?

Course Q&A Machine Learning Specialization Supervised ML: Regression and Classification
1

I watched the videos about the about the Loss function and the cost function, and now moved to the gradient decent implementation but I am having a hard time understanding the intuition behind gradient decent here.

My problem is I can not imagine how does the cost function is convex. can someone elaborate more on how the cost function here is convex and how choosing a -w and +w that are the same distance from the optimal w, will lead to the same cost?

2

Proving that the logistic cost function is convex requires use of some calculus, to compute the partial derivatives of the cost with respect to w.