For what values of x?

Question

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

Answer 1

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