1) Use the definition of derivative to show that function y = g(x) implicitly defined by equation: is not differentiable at point (0,1)

2) Find all points at which the tangent lines to the curve are horizontal for equation

3) Let , Show that

These questions are from my university's past exams. It won't be much problem for me, IF they give me more time to solve it... The first two problems are given like only about 10 minute to solve, and the last one is not even 5 minute (Given 180 min for 17 problems, but last one is like part a of the problem)

So, it either means 1) I am doing it the long way through, or 2) the university examiners don't expect anyone to pass the exam... Therefore, I want to ask for opinions on how to solve these types of complex questions in a more time-efficient way.

PS: I used 1-2 hours just to pull that lim h -> 0 of from the first problem