Question

Use the first derivative test to find local extrema Question h(x) = x3 + 32x2 + 120x + 9 Given the function above, use the First Derivative Test to find the local extrema. Select the correct answer below: There is a local minimum at x = -5 and a local maximum at x = -3. O There is a local minimum at x = -3. O There are no local extrema. O There is a local maximum at x = -5 and a local minimum at x= -3. O There is a local maximum at x= -5 and a local maximum at x= -3.

Answer 1

Answer o 3 . (a) = n3 14 .: 6() = x++39x?+nox+9 differention n'(x)= 84++ 32.23'+120x0 =n'(x) = gx?+ 64x+120 @ for critical point hica so → 82 +64x+120 = 0 ? + 3x +15=0 - 8+ V 89-4.1.15 by shreedharicharya method) 2.1 -8 164-80 +-878 = -41 -8+. - = -4 +1 → X=-3,-5 @ 00, -5 -3 ... first derivative test for relative maximum and Relative minimum at is relative maximum at a=c of & txiro before x=( li rcxito at a=( (ii f'(a) co affer x=( and t is relative minimum at and if i rcalco before a=d . li f(xico at x=d (iii) f'(x) >o after a=d

here falso when at 1000,-5) and f'casco when at (-5, #3) - and f'casso when xe (-3,00) so here x=-3 is docal minimum point and airs is local maximum point. Answer