Question

What is the smallest possible slope for a tangent line to the grap of the equation y=x^3-3x^2+5x

Answer 1

Here is what I have so far...
y'=3x^2-6x+5

Answer 2

\[Slope of \tan-line: y=k(x-x_0)+y_0\]

Answer 3

\[where: k=y'(x_0)\]

Answer 4

the graph of y' is a parabola, then it has a minimum value since its turned upwards, so the only thing you need to do is find the minimum value of the parabola.