Machine learning on Big data

I just viewed the webinar conducted by SkyTree. This particular slide has some information about the evolution of Machine Learning.

Screen Shot 2014-04-15 at 9.14.24 PM

Gradient checking quiz

Let J(\theta) =  \theta^3. Furthermore, let \theta = 1 and \epsilon=0.01. You use the formula

(J(\theta+\epsilon )-   J(\theta-\epsilon))/2\epsilon

to approximate the derivative. What value do you get using this approximation ?(When \theta=1,the true, exact derivative is
d/d\theta J(\theta) = 3 ).

The Octave code that I used to solve this is