### Calculus meets Functions

Many ways problem

The curve is increasing for $x>1$ Has a local minimum with
$y$-coordinate $1$
Has a point of inflection when $x=0$
Has a stationary point at $(1,1)$ $y=x^3+3x^2-9x+6$ $y=(x-1)^2+1$ $y=3x^4-4x^3+2$
Has a local maximum when $x=-3$ $y=x^3+3x^2-9x+6$ $y=2x^3+9x^2+1$ $y=1-\dfrac{1}{4}x^4-x^3$
Has an odd number of stationary points $y=7(x-1)^2+1$ $y=(x+4)^2+1$ $y=x^5-x^3+5$