Question

Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

f(x) = x³ + 9x² − 81x

Answer 1

f(x) = x3 + q x² 81x f'69 = 3*+10-101 1 f'(X) = 3x2+10x-81 7 for critical numbers Junction 3x²+ 10x dl=0 x ²4 6x-28 =0 X?+ 9x-3X – 22 = 0 *(X+9) -3(x+9) ab AI QUAD CAMERA 9) (x-3) =0

elthen X+9 = 6 [x=-91 X-3 20 [x=3) Calculating t o filan = 6*418 at x = -9 f(x) = -54+18=-36 <D Therefore maxima at x = -9 at x=3 f(x) = 10 to 360 O AI QUAD CAMERAinéma at sa OO REDMI NOTE 8

11 maxinuum nalle y fx at tangan f697 = €993 + q (+972-8 1-9 E-729 +229 +729 = 729 minimum values of for at x =43 163) = 3934 9039 281682 = 24 + 01-243 Thor foor crésical number of for) (-9, 729), (3, -135) OO REDMI NOTE 8 AI QUAD CAMERA