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Considerthefunctionf(x)=xx;x>0.(a)Findf0(x)andf00(x).(b)Solvef0(a)=0.Isthereanyb>0suc...
Consider the function f(x) = xx; x > 0.
(a) Find f0(x) and f00(x).
(b) Solve f0(a) = 0. Is there any b > 0 such that f00(b) = 0?
(c) It is clear that f0(x) < 0 for x < a and f0(x) > 0 for x > a. Therefore f is decreasing on
(0; a) and increasing on (a;1) and so f is not 11. Let g(x) = xx; x > a. Explain why g
is 11.
(d) Find (g1)0(4). 展开
(a) Find f0(x) and f00(x).
(b) Solve f0(a) = 0. Is there any b > 0 such that f00(b) = 0?
(c) It is clear that f0(x) < 0 for x < a and f0(x) > 0 for x > a. Therefore f is decreasing on
(0; a) and increasing on (a;1) and so f is not 11. Let g(x) = xx; x > a. Explain why g
is 11.
(d) Find (g1)0(4). 展开
1个回答
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(1)f'(x)=2x.f"(x)=2
(2)f"(x)=2为常数，不存在f"（b）=0
(3)f(x) = xx=0，x=0。a=0
(2)f"(x)=2为常数，不存在f"（b）=0
(3)f(x) = xx=0，x=0。a=0
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