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 , sof attains its minimum atx=5 and the minimum value isf(5)=-89
f^('')(-1) = -18 < 0 , sof attains its maximum atx=-1 and the maximum value isf(-1)=19