rx) =x\"-32x2 + 9 (a) Find the interval on which fis increasing. (Enter your ans
ID: 2888190 • Letter: R
Question
rx) =x"-32x2 + 9 (a) Find the interval on which fis increasing. (Enter your answer in interval notation.) Find the interval on which f is decreasing. (Enter your answer in interval notation.) oo,- 4) u (0,4) (b) Find the local minimum and maximum values of f local minimum-247 local maximum (c) Find the inflection points (x, y) (x, y) = Find the interval on which fis concave up. (Enter your answer in interval notation.) smaller x-value) (larger x-value) Find the interval on which fis concave down. (Enter your answer in interval notation.) Talk to TutorExplanation / Answer
c)
f(x)=x^4-32x²+9
f'(x) = 4x^3 -64x
f"(x) = 12x² -64
To find inflection point, set f"(x) =0
12x² -64 =0
4(3x² -16) =0
3x² =16
x= -4/3 , 4/3
hence inlection points are
(-4/3 , -1199/9)
(4/3 , -1199/9)
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Concave up when f"(x) >0, hence in inerval
(-, -4/3) U (4/3 ,)
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Concave down when f"(x) <0, hence in inerval
(-4/3 , 4/3)
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