How many real solutions does the equation $x^{3} - 3 x + 4 = 0$ have?

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Find the $x$ -coordinates of the stationary points of $f (x) = x^{3} - 6 x^{2} + 9 x$ .
On which interval is $f (x) = x^{3} - 6 x^{2} + 9 x$ strictly decreasing?
What is the local maximum value of $f (x) = x^{3} - 6 x^{2} + 9 x$ ?
Where is the point of inflection of the graph of $f (x) = x^{3} - 6 x^{2} + 9 x$ ?
Find the greatest and least values of $f (x) = x^{3} - 3 x^{2}$ on the interval $[- 1, 3]$ .
A square sheet of side $12$ cm has a square of side $x$ cm cut from each corner, and the sides are folded up to form an open box. What is th…