9:57 PM Wed Oct 834%Names:12.3.4.5.Chapter 2, Worksheet 2Directions: Please do all of the problems on this sheet, which is worth 100 points. Someone should be responsible for submitting your completed work into Gradescope. Enjoy!Suppose you watch a UFO in the sky for a while as it bounces around in the sky. You conclude from your observation that its elevation above the ground (measured in meters) after t seconds iss(t)=-t3-5t4t220(a) Find a graphing calculator and draw a graph of this function. Please try to not be sloppy as having a good graph will be a benefit to have for our other tasks.(b) Compute s'(t).(Using a different notation, you might also call this dsdt.) This is the vertical velocity of the UFO. What are the units of s'(t)? This problem asks you to do a fair amount of algebra.(c) There are two times where the velocity of the UFO is zero. Find these two times. (These also happen to be places where the UFO changes from losing elevation to gaining it, or vice versa.) You may need to use the quadratic formula, and you might consider looking at the graph to get a sense for where these numbers might be.(d) Compute s''(t).(Using a different notation, you might also call this d2sdt2.) This is the vertical acceleration of the UFO. What are the units of s''(t)? This problem also asks you to do a fair amount of algebra.(e) The UFO crash lands at time t=4. What is its velocity and acceleration when it hits the ground?Consider the following graph between the values x=-2 and x=3 :(a) On what intervals is this function increasing? (Approximate answers are okay for this problem.)(b) On what intervals is this function decreasing?(c) On what intervals is this function concave up?(d) On what intervals is this function concave down?