5 points SCalcET8 4.3011 Consider the equation below. (If an answer does not exi

Question

5 points SCalcET8 4.3011 Consider the equation below. (If an answer does not exist, enter DNE.) f(x) -s0x2 2 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection points. (x, y) = (smaller x-value) (x, y) = largerx-value) Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down.(Enter your answer using interval notation.) Need Help?WchTalk to Tutor Talk to a Tutor

Explanation / Answer

y= x^4-50x^2+2

Find derivative as

dy/dx = 4x^3 -100x

To find critical point, set dy/dx =0 and then solve for x as

4x^3 -100x = 0

4x (x² -25) =0

4x (x+5) (x-5) = 0

x = -5,0, 5

Find second derivative as

y" = 12x² -100

12x² -100 =0

x² = 100/12

x² = 25/3

x = -5/3 , 5/3

a)

Increasing on (-5,0)U(5,)

Decresaing on (-, -5)U(0,5)

b)

local minimum is -623

local maximaum is 2

c)

Inflection points are

(-5/3 , -3107/9)

(5/3 , -3107/9)

Concave up : (-, -5/3) U(5/3 ,)

Concave down : ( -5/3 , 5/3)

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