Hello I need some help with these 8 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. Calculate the Average Rate of Change (AROC) between x=-3 and x= 5 for the function f(x)=-x-+4x+1. (2 marks) 2. Calculate the Instantaneous Rate of Change (IROC) at x=/ for the function f(x)= -x-+4x+/. Do this calculation twice, using two different numerical approximations for Ax that are very close to x = 1. Sketch/Insert a graphical representation of this calculation (use DESMOS, if necessary). (5 marks) 3. What is the average rate of change between x and x+/ for the function S (x) - 25+4 Develop an expression, in terms of x, to show this average rate of change. Simplify the expression. (4 marks) 4. For the function f(x)=>'-&x+3 , calculate [(a+h)- f(@) where a=5 and a. h=2 b. h=1 c. h=0.5 d. h=0.1 Simplify the expression before substituting. (4 marks) 5. Evaluate the following limits. (6 marks) lim x2+x-2 X -2 x2-4 b) lim Vx -1 lim ( 3-8) x 1 x-1 6. Graph the function f(x) = x - x+ 1 i) Find approximate x values for max/min points. ii) Set up a table showing intervals of increase or decrease and the slope of the tangent on those intervals. lil) Set up a table of values showing "x" and its corresponding "slope of tangent" for at least 7 points iv) Sketch the graph of the derivative using the table of values from ill) ( 5 marks) 7. Find the derivative of the following functions using the lim (x+h)- f(x) a. f(x) = 10x4 b. f(x) = = 2x2 Show all your steps. (4 marks) 8. A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression h(t) = 98t - 4.91 . a. What the average rate of change for the first 2 seconds. b. At what point does the rocket reach its maximum height? Show a graphical and algebraic solution. c. Over what intervals is the rocket's height increasing and decreasing