Question

How do I explain to someone that
y=1/(x^2) has no horizontal tangents

Answer 1

I told the tadpole to take the derivative of the function

Answer 2

I told the tadpole that if you set it equal to zero, you can't solve that function

Answer 3

@satellite73

Answer 4

need help here at the school of frogs

Answer 5

That explanation works. Show that dy/dx = 0 has no solutions

In an informal way you could explain it like this

The graph of 1/(x^2) gets closer and closer to the x axis as x gets larger. It never hits the x axis. If you had a horizontal tangent, then that would either imply you have a flat part or a turning point. You can't have a flat part because it keeps getting closer and curving to the x axis. You can't have a turning point because again, it's getting closer and not turning away

Answer 6

Thanks my tadpole is annoying (ok this one is really mine)
Thanks alot Jim

Answer 7

no problem