The function f(x) = e^3x +6x^2 +1 has a horizontal tangent at x =?

[meredith]

Homework Statement

i can't solve it!
im really lost. i know you find f''(x) (i got 9e^3x +12) but i don't know where to go from there
what would i do on my calculator?

 

[praharmitra]

to calculate the horizontal tangent you only need to solve for f ' (x) = 0. f '' (x) is used and further derivatives are used to check whether that particular solution of the first equation gives a maxima, minima or an inflexion point.

Solve 3e^(3x) + 12x = 0

 

[HallsofIvy]

And that equation you will need to solve numerically, perhaps by graphing it on your graphing calculator and "zooming" in where it crosses the x-axis.