Three litres of milk cost r29,95 at shop a and two liters of milk cost r15,95 at shop
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1. The function 
is a parabola of the form 
. The the formula for the axis of symmetry of a parabola is 
. We can infer from our function that 
and 
, so lets replace those values in our formula:
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
or 
or 
From our previous point we know that the ball reaches its maximum time at
, which means that <span>it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.</span>
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
From our previous point we know that the ball reaches its maximum time at
(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when and
, and because the velocity function is continuous, you need only check the sign of
for values on the intervals (0, 3) and (3, 6).
We have, for instance and
, which means the particle is moving the positive direction for
, or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
which follows from the definition of absolute value. In particular, if is negative, then
.
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so is the derivative of
:
Compute the acceleration at seconds:
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)