Question

3rd derivative of f(x)=x

Answer 1

i know dy/dx=1, d2y/dx^2=0, but then what next?

Answer 2

The derivative of zero is... get this... zero!

Answer 3

sigh, so that's it?

Answer 4

http://www.wolframalpha.com/input/?i=derivative+of+zero

There's like proof and stuff. Also, remember y''=0 is still a constant. Constant means no slope.

Answer 5

now i'm going to ask out teacher why he gave us that

Answer 6

Yep. If you graphed y=0, you could see that it is a horizontal line, slope 0

Answer 7

You can prove it directly from the definition of a derivative. Let \(f(x)=0\) then
\[f'(x)=\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}=\lim_{h \to 0}\frac{0-0}{h}=\lim_{h\to 0}0=0.\]