For what values of x is #f(x)=(7x-1)(x-6)(x-2)# concave or convex?

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For what values of x is #f(x)=(7x-1)(x-6)(x-2)# concave or convex?

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Answer 1 · 2016-11-04T06:43:49

#f(x)=(7x-1)(x-6)(x-2)# is concave down on the interval #x<19/7#, and #f(x)# is concave up on the interval #x>19/7#.

Explanation:

#f(x)=(7x-1)(x-6)(x-2)#
Find first derivative:
#f'(x)=21x^2-114x+92#
Find second derivative:
#f''(x)=42x-114#
#f''(x)=6(7x-19)#
Find where second derivative is negative to get intervals of concave down, and where #f''(x)# is positive is where #f(x)# is concave up.
#f''(x)# is positive when #x>19/7#, and #f''(x)# is negative when #x<19/7#.

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For what values of x is #f(x)=(7x-1)(x-6)(x-2)# concave or convex?

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