The actual question is: Let C be a large number. Divide it into n equal parts: C/n.
Multiply together all those parts. what value should n be so that this product is maximized? (hint:You will need to wait until we consider logarithmic differentiation). My teacher gave me y=(c/x)^x but I don't know where to go from here. If you could help that would be awesome!
Multiply together all those parts. what value should n be so that this product is maximized? (hint:You will need to wait until we consider logarithmic differentiation). My teacher gave me y=(c/x)^x but I don't know where to go from here. If you could help that would be awesome!
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Find when dy/dx = 0
y = (c/x)^x
ln(y) = x * ln(c/x)
ln(y) = x * ln(c) - x * ln(x)
dy/y = ln(c) * dx - x * dx/x - ln(x) * dx
dy/y = dx * (ln(c) - 1 - ln(x))
dy/dx = y * (ln(c) - 1 - ln(x))
dy/dx = y * (ln(c/x) - 1)
dy/dx = 0
y = 0
(c/x)^x = 0
This never happens
ln(c/x) - 1 = 0
ln(c/x) = 1
c/x = e^1
c/x = e
c = x * e
x = c/e
y = (c/x)^x
ln(y) = x * ln(c/x)
ln(y) = x * ln(c) - x * ln(x)
dy/y = ln(c) * dx - x * dx/x - ln(x) * dx
dy/y = dx * (ln(c) - 1 - ln(x))
dy/dx = y * (ln(c) - 1 - ln(x))
dy/dx = y * (ln(c/x) - 1)
dy/dx = 0
y = 0
(c/x)^x = 0
This never happens
ln(c/x) - 1 = 0
ln(c/x) = 1
c/x = e^1
c/x = e
c = x * e
x = c/e
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What?