Find the greatest and the least values of the following functions.
$f (x) = {2.3}^{3 x} - {4.3}^{2 x} + {2.3}^{x}$ on the interval [-1, 1].

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Solution

$f (x) = {2.3}^{3 x} - {4.3}^{2 x} + {2.3}^{x}$
$f^{'} (x) = {6.3}^{3 x} - {8.3}^{2 x} + {2.3}^{x} = 0 \Rightarrow {2.3}^{x} ({3.3}^{2 x} - {4.3}^{x} + 1) = {2.3}^{x} ({3.3}^{x} - 1) (3^{x} - 1) = 0$
$x = - 1, 0$
$f (0) i s t h e l e a s t v a l u e a n d f (- 1) i s t h e g r e a t e s t v a l u e$

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