- #1
Karol
- 1,380
- 22
Homework Statement
$$y=a\cdot x\cdot ln\left(\frac{b}{x}\right)$$
The derivative should be 0 (to maximize), what's x?
Homework Equations
$$(ln\:x)'=\frac{1}{x}$$
$$(x^a)'=ax^{(a-1)}$$
$$(uv)'=u'v+v'u$$
The Attempt at a Solution
$$\dot y=a \left[ ln \left( \frac{b}{x} \right)-x\frac{x}{b}x^{-2} \right]=a \left[ ln \left( \frac{b}{x} \right)-\frac{1}{b} \right]$$
$$\dot y=0 \rightarrow ln \left( \frac{b}{x} \right)-\frac{1}{b}=0 \rightarrow x=e^{\left( \frac{1}{b} \right)}$$
But the answer should be ##x=\frac{b}{e}##
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