Which points on curve are tangents horizontal? (1 Viewer)

[enak101]

y=2x^3-9x^2-60x+3

I have to find points where tangents are horizontal.

If tangents are horizontal that means the gradient is 0?

I'm not sure how to go about this.

y'=9x^2-18x-60 is the derivative of the line. Not really sure. Do I sub in x=0?

y'=0-0-60
y'=-60 lol, no idea.

 

[Trebla]

By the way the derivative should be
y' = 6x² - 18x - 60

You solve y' = 0. In other words solve the quadratic equation
6x² - 18x - 60 = 0

 

[Carrotsticks]

The tangent being horizontal is equivalent to a stationary point, so we have

6x^2 - 18x - 60 = 0

x^2 - 3x - 10 = 0

(x-5)(x+2) = 0

x=-2, 5

Then sub back into the original equation for the y values.

 

[enak101]

Sorry, I don't know how I overlooked that, I just made that mistake in forum post

Thanks for the help