NARRATOR: Exercise seven.
Let f(x) = x cubed plus x – 2.
Show that f(x) has no stationary points.
So we know that stationary points occur
when the derivative is equal to 0.
So let's first consider the derivative of this function.
So f dash x is equal to 3x squared + 1.
And for stationary points, we need the derivative to be equal to 0.
So we have a quadratic equation here.
So we can think about the discriminant of this equation.
And the discriminant we know is b squared – 4ac
which in the case of this equation is 0 squared – 4 times 3 times 1.
So we have a discriminant of –12.
So that tells us that f dash x = 0 has no solutions ...
... since we know that the discriminant is negative.
So therefore, if the f dash x = 0 has no solutions,
that means f(x) has no stationary points.