Question

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(1 point) Book Problem 27 Consider the function f(x) = 12x5 + 15x4 - 240x3 + 6. This function has 3 critical numbers A <B<C: B = and C= A= At these critical numbers, tell whether f(x) has a local min (type in LMIN), a local max (LMAX), or neither (NEIT at B and at C At A f(x) has inflection points at (reading from left to right) x = D, E, and F: E = , and F = D= Tell whether f(x) is concave up (type in CU) or concave down (type in CD) on the following intervals: On (-0, D): on [D,E): on [E.F] : and on [F,00): 1

Answer 1

fla)= 1245+ 15x4 - 240x3 +6 f'(x)= 60x4 + 6003 - 720 x2 For Critical points flra)=0 T 60x4 +603-720 x2=0 60x2 x2 + 4x -3x-12}=0 ( [22 ㅋ 22+x-12] = 0 7 60x2 7 6022 ( 24474) -3(2+4)) 50 g boxe (2-3) (2+4)=0 x=0, x=3, 224

This function has 3 critical numbers ACB cc: 3 c - A = -4 B = Now local Minima + 3 local Maxina -4 o Trotterties print (Neither Miniona nor At these critical Numbeos, tell whether flx) has a maxima) min (type in LMIN), a local local max (2Max, or neither NETH LMIN At С A BINETH LMAX Now f (x) = 240x3 +180x2 -14402 = 0 3 60x [42 2 + 3x-24] = 6ox (4a2 + 3x - 24) 50 П a ano 4x2 +3a-2420 ana ~37 Jatux uxd4 2 x4 3 7 J9+16xd4 -3 £ J9 + 384 8 8. 7x= - 3£ 393 => x = 0, 3 +5393 -3-5393 8 8 8

fla) has inflection points at x=D, EIF D = 3-5393 F = -3 + 393 8 8 Now , + + F D E on (-os ID) TCD [DE] CU CE,P] : C D n CU [Fico):