For each function, find the points on the graph at which the tangent line is horizontal. If none exist, state that fact. y=xcubed-2

answer: The points on the graph where the tangent line is horizontal are precisely the points where first derivative is 0. Here, we have f(x)=x^3 - 2 So, f'(x)=3x^2 f'(x)=0 implies 3x^2=0 which is possible only when x=0. Therefore, x=0 is the only point on the graph of f(x)=x^3 - 2 where the tangent line is horizontal.