What are the critical values, if any, of $f(x)= -2 x^3 + 27 x^2 - 48 x + 7$ ?

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Answer 1 · 2015-12-23T20:51:43

$c=1,8$

A critical value is the $x$ -value at which $f'(x)=0$ or does not exist.

Find $f'(x)$ .

$f'(x)=-6x^2+54x-48$

Find when $f'(x)=0$ .

$-6x^2+54x-48=0$
$=>-6(x^2-9x+8)=0$
$=>-6(x-1)(x-8)=0$
$color(red)(x=1,8$

Find when $f'(x)$ does not exist.

$f'(x)$ is defined for all $x$ .

Thus, the only critical values are $c=1,8$ .

graph{-2 x^3 + 27 x^2 - 48 x + 7 [-5, 15, -289.3, 405]}

What are the critical values, if any, of f(x)= -2 x^3 + 27 x^2 - 48 x + 7f(x)= -2 x^3 + 27 x^2 - 48 x + 7?