PaA liple Choice Carcle the correct answer 7. The largest intarval over which /\

Question

PaA liple Choice Carcle the correct answer 7. The largest intarval over which /'s lncreasing for e) ( sy C. (-00,5 B. I-5,0o) ?· The largest open interval over which /b concave up for f(z)-y B. (7,00) C. (-00, 0o) D. nowbere ? The function f(z)s er hue a point of infection with ,ooordinate of B. c C. 0 D. None exint The fauction fs A. points ol iufection at # m-98nd z-9. B. points of infection at 3 and :-3 C. apoint of inflection at = 0 D. no point of infiection Determine the soordinate of each critical point of f(s)-VE- A. 0 B. 5 D. None exist 6. f(x)+z +7 has A relative maximum a: --2 Creative maximum at # 2 B.relative minimum at 2 D, relative minimum at z = 2 7. f(z) = 2-16 has A. no relative maximum; a relative minimum at z4 B. a relative maximum at z4 no relative minimum C. relative minima at :--4 and # 4i , relative maximum at 1-0 D. relative maxima n: =-16 and? 1&a; relative minimum at

Explanation / Answer

1)
[5 , inf)

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2)
On this one i dunno the index of the root...
IS that fourth root or third root etc?

But here it is ...

If it is cuberoot, then option A
If it is 4th root, then nowhere
If it is 5th root, then option A
If it is 6th root, then nowhere

So, if the index of root is even, then NOWHERE--> option D
If index of root is odd, then option A

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3)
e^(x^4)

Deriving :
4x^3*e^(x^4)

Deriving again :
f'' = 4(3x^2e^(x^4)) + 4x^6*e^(x^4)) = 0

Solvin', we get x = 0

But it remains concave up everywhere

So, no inflection point

Option D

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4)
x^2 / (x^2 - 9)

Deriving twice:
y'' = 54(x^2 + 3) / (x^2 - 9)^3

Equating to 0 :
54(x^2 + 3) = 0

x^2 + 3 = 0

No oslution

So, option D

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