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Trava [24]
3 years ago
8

Find the points on the curve y = 2x3 + 3x2 − 12x + 6 where the tangent line is horizontal.

Mathematics
1 answer:
Orlov [11]3 years ago
3 0
N.b., this is copied from an answer I wrote for someone else.

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

First, differentiate y.

y'=6x^2+6x-12

Next, find the zeros of y' by factoring.

6(x^2+x-2)=0 \\ x = -2, x = 1

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

(-2,21), (1,-6)
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