已知函数F(X)=X2-4X-5,求当X属于[-3,0],[3,5],[1,4]的最值
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已知函数F(X)=X2-4X-5,求当X属于[-3,0],[3,5],[1,4]的最值
F(x)=x^2-4x-5
F'(x) = 2x
F''(x) =2 (min)
F'(x) = 0 => x=0
F(0) = -5
for x∈[-3,0]
max F(x) = F(-3) = 9+12-5 =17
min F(x0 = F(0) = -5
for x∈[3,5]
maxF(x) = F(5) = 25-20-5 = 0
minF(x) = F(3) = 9-12-5 = -8
for x∈[1,4]
maxF(x) = F(4) = 16-16-5 = -5
minF(x) =F(1) = 1-4-5 = -8
F'(x) = 2x
F''(x) =2 (min)
F'(x) = 0 => x=0
F(0) = -5
for x∈[-3,0]
max F(x) = F(-3) = 9+12-5 =17
min F(x0 = F(0) = -5
for x∈[3,5]
maxF(x) = F(5) = 25-20-5 = 0
minF(x) = F(3) = 9-12-5 = -8
for x∈[1,4]
maxF(x) = F(4) = 16-16-5 = -5
minF(x) =F(1) = 1-4-5 = -8
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