It looks like you've uploaded a photo containing a math problem related to the position, velocity, and acceleration of an object. The problem involves analyzing functions and intervals.

Let's break down the tasks from the problem based on the given image:

The position function is given as:
$f(t) = t^3 - 9t^2 + 24t$, where $0 \leq t \leq 6$.

1. When is the object stationary?
   An object is stationary when its velocity is zero. So we need to find when the derivative of the position function (velocity) is zero.

2. When is the object moving to the right?
   The object moves to the right when the velocity is positive. After finding the velocity function, we determine the intervals where it is positive.

3. When is the object moving to the left?
   The object moves to the left when the velocity is negative. Again, after finding the velocity, we analyze the intervals where it is negative.

4. Determine the velocity and acceleration at $t = 1$.
   The velocity is the first derivative of the position function, and acceleration is the second derivative. By calculating both at $t = 1$, we find the answers.

5. On what intervals is the speed increasing?
   Speed increases when the velocity and acceleration have the same sign. We check the intervals where this condition holds.

Let me know if you need help going through any of these steps, or if you'd like me to perform the calculations directly!