Answer
$y = 3x - 1$
Work Step by Step
In order to find the equation of a tangent line, first you need to take the derivative. For this equation, just use the Power Rule.
$y=3x^{2}-x^{3}$
Power Rule: $\frac{dy}{dx} = nx^{n-1}$
$\frac{dy}{dx} = 3(2)x-(3)x^{2}$
$\frac{dy}{dx}=6x-3x^{2}$
The derivative is your equation of the slope. To find the slope at the point (1,2), plug in x=1 into the derivative equation:
$\frac{dy}{dx} \Bigr|_{\substack{x=1}}=6(1)-3(1)^{2} = 3.$
Now to get the equation of the tangent line, use point-slope form:
$y-y1 = m(x-x1)$
$y-(2) = (3)(x-(1))$
$y = 3x-3-2$
$y = 3x - 1$
