The function , has
A. two points of local maximum
B. two points of local minimum
C. one maxima and one minima
D. no maxima or minima
Let
Apply first derivative and get
Apply derivative,
Put f'(x)=0, and get
Split middle term and get
Now we find the values of f(x) at x=-1, 2
Hence from above we find that the point of local maxima is x=-1 and 11 is the maximum value of f(x).
Whereas the point of local minima is x=2 and -16 is the minimum value of f(x).
So, the correct answer is option C.
Hence, the given function has 1 minima and 1 maxima.