Open Question: The graph of the function F(x)=-(x-5)^3 is concave upward in what interval?
7:43 Publicado por Flechado16
F(x)=-(x-5)^3
F'(x) = -3(x-5)^2
F''(x) = (-3)(2)(x-5)
F''(x) = -6(x-5)=0
F'(x) = -3(x-5)^2
F''(x) = (-3)(2)(x-5)
F''(x) = -6(x-5)=0
x=5 is a point of inflection
Test for concavity:
Consider the intervals (-8 ,5), (5, 8)
choose any one point from each of the intervals.
if F''(x) < 0 , F(x) is concave down on that interval
if F''(x) > 0 , F(x) is concave up on that interval
F''(x)= -6(x-5)
(-8 ,5): choose x=1; F''(1)=24 > 0, f is concave up on (-8 ,5):
(5, 8): choose x=6; F''(1)=-6 < 0, f is concave down on (5, 8):
F is concave up on (-8 ,5):
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