What are the local extrema, if any, of #f (x) = x^3 - 6x^2 - 15x + 11 #?
1 Answer
Maxima=19 at x=-1
Minimum=-89 atx=5
Explanation:
#f(x) = x^3-6x^2-15x+11#
To find the local extrema first find the critical point
#f'(x) = 3x^2-12x-15#
Set
#3x^2-12x-15# =0
#3(x^2-4x-5)# =0
#3(x-5)(x+1)=0#
#f^('')(x)=6x-12#
#f^('')(5)=18 >0# , so#f# attains its minimum at#x=5# and the minimum value is#f(5)=-89#
#f^('')(-1) = -18 < 0# , so#f# attains its maximum at#x=-1# and the maximum value is#f(-1)=19#