vertical tangents and cusps (1 Viewer)

[Masaken]

are you able to tell just from a given equation of a curve whether it has a vertical tangent or cusp?? if so, how?

 

[chilli 412]

if there are any vertical asymptotes in a function you cant take the derivative there, also if you take the derivative of a function and then plug in an x value where you end up with a zero in the denominator youll end up with a vertical tangent, e.g f(x) = x^(1/3)
f'(x) = 1/(3x^(2/3)), and f'(0) is undefined other than that its hard to tell from an equation