How do you use the first and second derivatives to sketch y = x^3 - 12x - 12?

1 Answer
James C.
Feb 1, 2016

See the answer bellow.

Explanation:

y=x^3-12x-12
First derivative: y'=3x^2-12
Second derivative: y''=6x

Using y'=3x^2-12
3(x^2-4)
3(x-2)(x+2)
x=-2,2
Sub x values into y=x^3-12x-12, to find y values
y=(-2)^3-12(-2)-12
y=4, (-2,4)
y=(2)^3-12(2)-12
y=-28, (2,-28)

Using y''=6x
Sub x values into y''=6x
6(-2)=-12
x<0
:. (2,-28) is a maximum point
6(2)=12
x>0
:. (-2,4) is a minimum point

When x=0
y=0^3-12(0)-12
y=-12
(0,-12)

Use the information from the first and second derivative to sketch the graph as well as the y intercept.

graph{y=x^3-12x-12 [-10, 10, -5, 5]}

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