Question

Please answer with work

Determine all critical points for the function. 9) f(x) = x3 - 9x2 + 8 9) A) X = -3 and x = 3 B) x = 0 and x = 3 C) x = 0 D) X = 0 and x = 6

Answer 1

$f\left ( x \right )=x^{3}-9x^{2}+8$

$f{}'\left ( x \right )=\frac{\mathrm{d} }{\mathrm{d} x}\left [x^{3}-9x^{2}+8 \right ]$

$=\frac{\mathrm{d} }{\mathrm{d} x}\left [x^{3} \right ]-\frac{\mathrm{d} }{\mathrm{d} x}\left [9x^{2} \right ]+\frac{\mathrm{d} }{\mathrm{d} x}\left [8 \right ]$

= 3.rº 9x [22] + 0 d.c

$=3x^{2} -9\times 2x$

$f{}'\left ( x \right )=0$

$\Rightarrow 3x^{2} -18x=0$

$\Rightarrow 3x\left ( x-6 \right )=0$

$x\left ( x-6 \right )=0$

$x=0$ or $x-6=0$

$x=0$ or $x=6$

That is

Function have critical points at $x=0,6$

Correct option is

D) x = 0 and x =

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