Application of DerivativeHard
Question
For the function f(x) = x4 (12 ln x - 7)
Options
A.the point (1, - 7) is the point of inflection
B.x = e1/3 is the point of minima
C.the graph is concave downwards in (0, 1)
D.the graph is concave upwards in (1, ∞)
Solution
f′(x) = 16 x3 (3ln x - 1)
f′(x) = 16 . 3 . x2 . 3. lnx
x = 1 is point of inflection. x = e1/3 is point of minima. In (0, 1) f(x) is concave downward. In (1, ∞) f(x) is concave upward.
f′(x) = 16 . 3 . x2 . 3. lnx
x = 1 is point of inflection. x = e1/3 is point of minima. In (0, 1) f(x) is concave downward. In (1, ∞) f(x) is concave upward.
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