Critical points

Recall that if a function [math]f[/math] is continuous and has a maximum or minimum at a point [math]c[/math] in its domain, then [math]f'\left(c\right)=0[/math] or [math]f'\left(c\right)[/math] does not exist. When these conditions are met, [math]c[/math] is called a critical point.[br][br]The graph below shows the function [math]f\left(x\right)=x^4+x^3-x^2-x-1[/math], the point A moves along the graph as you change the values of [math]a[/math], can  you identify the critical points of [math]f[/math]? What is the max/min of [math]f(x)[/math] on the intervals: [math]\left[-1.5,-0.39\right],\left[-1.4,1.1\right],\left[-1,0.64\right][/math] ?

Information: Critical points