If f'(a)=0, then the tangent of the function f at x=a is a horizontal line. if F(x)=f(x)*g(x) is differentiable at x, then both f and g are differentiable at x. limf(x) always equal to f(c). x>c If f is not continuous at x=a then f(x) is not differentiable at x=a. . If y=f(x) is differentiable at x=c then the tangent line to f at x=c is y=f(c) +f' (c)(x-c). If a function f has a vertical tangent at the point x=a, then f is not differentiable at x=a