Find all the critical points of the function 𝑓(𝑥) = 𝑥3 +6𝑥2 − 15𝑥 +7 and classify each of them as either local maximum(s) or local minimum(s)?

1 Answer
iceman
Apr 22, 2018

Please see the explanation.

Explanation:

#f(x)=x^3+6x^2-15x+7#
#f'(x)=3x^2+12x-15#
#3(x^2+4x-5)=0#
#(x+5)(x-1)=0#
#x=-5, 1# => critical points
#f(-5)=-125+150+75+7=107#
#f(1)=1+6-15+7=-1#
2nd derivative test to determine the nature of the critical points:
#f"(x)=6x+12#
#f"(-5)=-30+12=-18<0# => (-5, 107) local maximum
#f"(1)=6+12=18>0# => (1, -1)local minimum

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