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\f8. If the population growth (P) in a community is projected to follow the function P= 71+5t+350 (t is time in years), then find the instantaneous rate of growth in the 2nd year. 9. How many maximum or minimum points does the equation f(x)=-(x+4x-4)(x+2)(x -1) have? 10. Given the function f(x) = x , what is the value of x at the point where the slope of tangent line on this function is m = 27.1. Calculate the Average Rate of Change (AROC) between x=-3 and x= 5 for the function ((x)= -x-+4x+1. (2 marks) 2. Calculate the Instantaneous Rate of Change (IROC) at x= 1 for the function ((x)= -x+4x+1. 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)1. What is the average rate of change between x=3 and x=4 for the function f(x) = -x'+4x+1? 2. What is the simplified average rate of change between x=3 and x=3+h for the function f(x) = -x-+5 3. What is the graphical representation of the instantaneous rate of change? 4. For the function f (x) = - , calculate (to 5 decimal places) [(ath) = [@ where h 0 = 5 and h=0.1 5. What is the instantaneous rate of change for ((x)=2x+5 at x=-7 6. How is the average rate of change and the instantaneous rate of change related for ((x)=2x+5 7. If the population growth (P) in a community is projected to follow the function P(1) = 71+5t+350 (f is time in years), then find the average rate of growth from the 20 to the 3" year.\f8. 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 - 4.97. 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? ( 5 marks)7. Find the derivative of the following functions using the lim f ( x +h) - f(x) h a. f(x) = 10x 1 b. ((x) = = 2x2 Show all your steps. (4 marks)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. ili) Set up a table of values showing "x and its corresponding "slope of tangent" for at least / points. iv) Sketch the graph of tie derivative using the table of values from iin) ( 5 marks)