Answer to Question #17679 in Calculus for hsd

Question #17679
Let f(x)=2x^3−24x+2 Input the interval(s) on which f is increasing. Input the interval(s) on which f is decreasing. Find the point(s) at which f achieves a local maximum. Find the point(s) at which f achieves a local minimum. Find the intervals on which f is concave up. Find the intervals on which f is concave down. Find all inflection points.
1
Expert's answer
2012-11-02T10:22:42-0400
we must find f' and f''
f'=6x^2-24 f'=0 x=-2, x=2
f"=12x^2 f"=0 x=0
increase where f'>0 so at x from(-infinity, -2) and(2, +infinity) decrease where f'<0 so x from (-2 , 2) local maximum x=-2 local minimum x=2 concave up where
f"<0 concave down where f">0 12x^2>0 if x not zerox=0 is not inflection point because function does notchange type of concavity at x=0

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