Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (i) f(x) = x ^2 (ii) g(x) = x^ 3 – 3x
contexto.140
(i) Given:
and
Now
[Turning point]
Again, when , [Positive]
Therefore, is a point of local minima and local minimum value =
(ii) Given:
and
Now
or [Turning points]
Again, when ,
[Negative]
is a point of local maxima and local maximum value
And when [Positive]
is a point of local minima and local minimum value