So the problem goes like this:
Let f(x) be -x^3 at x<0 and x^3 at x>=0.
I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.
Yes...my teacher is a sadist
So the problem goes like this:
Let f(x) be -x^3 at x<0 and x^3 at x>=0.
I need to find the first derivative, second derivative, and the third derivative both the points which they are undefined and their graphs.
Yes...my teacher is a sadist
I'm a little confused by what you mean by "both the points which they are undefined". As you have written it this function is defined everywhere, and so are the derivatives.
To take derivatives of piecewise functions you take the derivative of each piece and keep the bounds on x the same.
For instance,
if f(x) = 2x for x<0 and f(x)=x^2 for x>=0 then
the first derivative will be
f'(x)=2 for x<0 and f'(x)=2x for x>=0.
Hope this helps with your problem!