What are the local extrema, if any, of #f (x) =(x^3−4 x^2-3)/(8x−4)#?
The given function has a point of minima, but surely doesnot have a point of maxima.
The given function is:
For critical points, we have to set, f'(x) = 0.
This is the point of extrema.
To check whether the function attains a maxima or minima at this particular value, we can do the second derivative test.
Since the second derivative is positive at that point, this implies that the function attains a point of minima at that point.