Question

Given f(x)=x^3−2x^2−8x find any point(s) of inflection y=f(x) may have.

Answer 1

`((2)/(3),-(160)/(27))`

Explanation:

Given:

`f(x)=x^(3)-2x^(2)-8x`

Required:

Determine the point of inflection of the given function.

`f'(x)=3x^(2)-4x-8`

`f^(11)(x)=6x-4=0`

`6x=4`

`x=(4)/(6)=(2)/(3)`

Substitute for x in the function.

`y=x^(3)-2x^(2)-8x=((2)/(3))^(3)-2((2)/(3))-8((2)/(3))=-(160)/(27)`

So, the point of inflection is:

`((2)/(3),-(160)/(27))`

Answer:

`((2)/(3),-(160)/(27))`