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Find the points on the curve y = 2x3 + 3x2 − 12x + 1 where the tangent line is horizontal. (x, y) = (smaller x-value) (x, y) = (larger x-value)

Respuesta :

susanwiederspan
Thinking about the graph of y, the rate of change is zero whenever there is an extremum.

First, differentiate y.

[tex]y'=6x^2+6x-12[/tex]

Next, find the zeros of y' by factoring.

[tex]6(x^2+x-2)=0 \\ x = -2, x = 1[/tex]

Now, we substitute these x-values into the original equation to find the coordinates. 

[tex](-2,21), (1,-6)[/tex]

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