Use the second derivative to determine the point of inflection for y = x3 – x2 – 8x + 12.

Use the second derivative to determine the point of inflection for y = x3 – x2 – 8x + 12.

 

 

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1st derivative: y'=3x²-2x-8=(x-2)(3x+4). Max, min, or inflexion occur when x=2 and -4/3.

2nd derivative: y''=6x-2, y''(2)=10 (minimum), y''(-4/3)=-10 (maximum).

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