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secondary 4 | A Maths
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Hi all, i need help with qn 13 pls help. would appreciate it greatly thanks!
Date Posted: 3 years ago
Views: 187
V = λx² ln(1/x)
= λx² ln x-¹
= -λx² ln x
Using product rule,
dV/dx = -λ(x² (1/x) + 2x ln x)
= -λ(x + 2x ln x)
= -λx(1 + 2ln x)
When speed is a maximum, dV/dx = 0
-λx(1 + 2ln x) = 0
-λx = 0 or 1 + 2ln x = 0
x = 0 (rejected as x cannot be 0 since that would make ln(1/x) and ln x undefined. It is also already given that 0 < x < 1)
or lnx = -½
x = e-¹/²
x = 1 / e¹/²
x = 1/√e
= λx² ln x-¹
= -λx² ln x
Using product rule,
dV/dx = -λ(x² (1/x) + 2x ln x)
= -λ(x + 2x ln x)
= -λx(1 + 2ln x)
When speed is a maximum, dV/dx = 0
-λx(1 + 2ln x) = 0
-λx = 0 or 1 + 2ln x = 0
x = 0 (rejected as x cannot be 0 since that would make ln(1/x) and ln x undefined. It is also already given that 0 < x < 1)
or lnx = -½
x = e-¹/²
x = 1 / e¹/²
x = 1/√e
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