Question

If you have a curve, what's tangent to the tangent line on the curve?

Answer 1

Second derivative, right?

Answer 2

yep

Answer 3

k thanks!

Answer 4

all tangent lines are tangent to themselves. but yes, the second derivative is tangent to the function of the slopes of tangent lines

Answer 5

Wait. Shouldn't it be tan(tan(f(x)))?

Answer 6

nah.

Answer 7

Ok.

Answer 8

if e = mc^2
then the second derivative is
f''(x).
for example
f(x) = x^3
e = mc^2
f'(x) = 3x^2
f''(x) = 6x
make sense?