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For what values of x?

For what values of x does the curve y^2-x^3-15x^2=8 have horizontal tangent lines? 
 
Answer: x=0 and x=-10

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Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Horizontal tangent means slope is zero; so 1st derivative is zero.
 
2yy' - 3x^2 - 30x = 0
 
y' = 0 so
 
3x^2 + 30x = 0
 
x(x + 10) = 0
 
x = 0, -10

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