Review question

# How many stationary points does $y = 2x^3 - 6x^2 + 5x - 7$ have? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9582

## Solution

The function $y = 2x^3 - 6x^2 + 5x - 7$ has

1. no stationary points;

2. one stationary point;

3. two stationary points;

4. three stationary points.

Differentiating, we find $y' = 6x^2 - 12x + 5.$

We could find the roots, but it is quicker just to notice that the discriminant of the quadratic $y'$ is $12^2 - 4\times 6\times 5 = 24 > 0$.

This means the equation $y' = 0$ has two distinct real roots, and hence the answer is (c).