In this problem, select all choices with correct answer$($s$).$

The tangent to the curve $y=x^2(\frac{1}{3}x-\frac{6}{2})+5x$ is horizontal when $x=?$

WARNING! An incorrect choice will invalidate a correct one.

Hint:

Distribute $x$ first.

Apply the difference, sum, and power rules: i$.$e$.,\frac{d}{dx}{x}^n=n{x}^{n-1}.$

The slope of a horizontal line is zero.

$($Set the derivative equal to zero and solve$).$

$1$

$2$

$3$

$5$