Text description - screencast for exercise 8

[The narrator reads out the onscreen text.]

NARRATOR: Exercise seven. Let f of x = x cubed plus x - 2. Show that f of 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 of x has no stationary points.