How do you find all points of inflection given y=-x^4+3x^2-4?

1 Answer
Mia
Nov 25, 2016

(1,-2) and (-1,-2)" " are two inflection points of the given function.

Explanation:

The inflection points of a function is determined by computing
" "
the second derivative of y then solving for color(blue)(y''=0).
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y=-x^4+3x^2-4
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y'=-4x^3+6x
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y''=-12x^2+6
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To find the inflection points we would solve the equation:
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color(blue)(y''=0)
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rArr-12x^2+6=0
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rArr-12(x^2-1)=0
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rArr-12(x-1)(x+1)=0
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rArrx-1=0rArrx=1" "
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Or
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x+1=0rArrx=-1
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The ordinate of the point of abscissa x=1 is:
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y_((x=1))=-1^4+3(1)^2-4=-1+3-4=-2
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The ordinate of the point of abscissa x=-1 is:
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y_((x=-1))=-(-1)^4+3(-1)^2-4=-1+3-4=-2
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Hence,
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(1,-2) and (-1,-2)" " are two inflection points of the given function.

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