Question

Sketch the graph of a function f for which f(0) = -1, f '(0)=0, f '(x) < 0 if x < 0, and f '(x) > 0 if x > 0

Answer 1

To sketch the graph of the function with an inequality. First is to analyze the different inequality.
If f(0) = 0 the line is in the center of the graph in the origin.,
if f(x)<0 the line is decreasing
if f(x)>0 the line is increasing.
I hope that i answered your question