The derivative of a function f(x) is the function whose value at x is f′(x). The graph of a derivative of a function f(x) is related to the graph of f(x). Where (f(x) has a tangent line with positive slope, f′(x)>0. Where (x) has a tangent line with negative slope, f′(x)<0. Where f(x) has a horizontal tangent line, f′(x)=0. If a function is differentiable at a point, then it is continuous at that point.