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Global Maxima

Set up an equ...

Question

Set up an equation of a tangent to the graph of the following function.
$y = (2 x - 1) e^{2 (1 - x)}$ at the point of its maximum.

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Solution

$y = (2 x - 1) e^{2 - 2 x}$
$\frac{d y}{d x} = 2. e^{2 - 2 x} - 2. (2 x - 1) e^{2 - 2 x} = 4 (1 - x) e^{2 - 2 x} = 0 \Rightarrow x = 1$
The equation of tangent at point of its maximum is $x = 1$ as the slope of tangent at maximum is $^{'} 0^{'}$

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