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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 Tutor

Explanation / 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)