Hi, I need help with these 3 questions please solve this questions with working out much appreciated:

Question 5.1 (6 marks) Consider the function f('f):m- a) Find all local extrema of f, and classify each as a local minimum or local maximum. b) Find the global minimum and global maximum values of f on the interval [1, 10]. If no such values exist, explain why not. ) Find the global minimum and global maximum values of f on the interval [10, 1]. If no such values exist, explain why not. Learning objectives (for your information only): Explain the relationship between the (local) maxima and minima of a function and its derivative, at least at the points at which the derivative exists. * Apply tests using derivatives to classify an extremum as a local maximum or a local minimum. * Identify global maxima and minima when possible Question 5.2 (4 marks) You are designing a rectangular box. You are given the requirement that the box must have a square base and open top and will be constructed from two types of material. The material used to make the bottom of the box costs $0.10 per square inch; the material used to make the rest of the box costs $0.06 per square inch. You have a total budget of $3.00 per box. Your task is to make the box with the largest volume you can. You quickly realise that to make a box of maximal volume, you will want to use as much material as possible. Accordingly, you formulate a plan where you will use all of the $3.00 budget to make the box. What are the dimensions of the box that will give you the largest volume? Learning objectives (for your information only): * Explain how to use the tools of calculus to identify global maximum. * Construct a suitable mathematical objective in a semipractical design question Question 5.3 (10 marks) Consider the two scenarios below involving rates of change. The two parts are completely independent of each other and are unrelated, except for the common theme of addressing relationships between rates of change. a) Two commercial airplanes are flying at 40,000 feet along straight-line courses that intersect at right angles. Plane A is approaching the intersection point at a speed of 442 knots (nautical miles per hour). Plane B is approaching the intersection at 481 knots. At what rate is the distance between the planes changing when A is 5 nautical miles from the intersection point and B is 12 nautical miles from the intersection point? b) The top of a solid wooden plank slides down a vertical wall at 24 in/s. When the bottom of the plank is 4 ft from the wall, it slides away at 18 in/s. How long is the plank? Learning objectives (for your information only): Illustrate how functional relationships between closely-related quantities can be used to evaluate their relative rates of change, and then applying that to some simple practical cases based on geometrical arguments