Use the graph of f to sketch a graph of f'. . . . . . Choose the graph of f'. I y=f(x) O A. 4- O B. 2 Ay X X O- X 2 -2- O C. OD. + Ay Hol 6- X Xf(x) - f(a) a. Use the definition mean = lim x- a - to find the slope of the line tangent to the graph of f at P. x -> a b. Determine an equation of the tangent line at P. c. Plot the graph of f and the tangent line at P. f(x) = x2 -9, P(5, 16) . . . . . a. mtan b. y = c. Choose the correct answer below. O A. O B. O c. OD. Ay Ay Ay A XThe limit below represents the slope of a curve y = f(x) at the point (a,f(a)). Determine the function f and the number a; then calculate the limit. 2(3 + h)# - 162 lim h-0 h . . . . . Determine the function f(x) and the number a. Choose the correct answer below. O A. f(x) = 2(3 + x)*; a= 3 O B. f (x) = 2(3 + x) 4; a=0 O c. f(x) = 2x*; a=0 O D. f(x) = 2x*; a = 3 Calculate the limit. 2(3 + h)# - 162 lim h -0 h (Simplify your answer.)Energy is the capacity to do work, and power is the rate at which energy is used or consumed. Therefore, if E(t) is the energy function for a system, then P(t) = E'(t) is the power function. A unit of energy is the kilowatt-hour; the corresponding units for power are kilowatts. The graph shows the energy demand function for a small community over a 25-hr period. Complete parts a through c. E , 450j ' q 4007/\\ 9' a i ii): i 350 , e 8 300 Lu 250 200 r> o 5 10 15 20 25 Time (hrs) t 3. Estimate the power at t= 10 hr. Choose the correct answer below. 0 A. The power at t= 10 hr is approximately 389 kW. 0 B. The power at t= 10 hr is approximately - 389 kW. 0 C. The power at t= 10 hr is approximately - 15 kW. 0 o. The poweratt=10 hr is approximately 15 kW. Estimate the power at t= 20 hr. Choose the correct answer below. 0 A. The power at t= 20 hr is approximately 10 kW. 0 B. The power at t= 20 hr is approximately - 339 kW. 0 C. The power at t= 20 hr is approximately 339 kW. 0 D. The power at t=20 hr is approximately - 10 kW. : b. At what time(s) on the interval [025] is the power zero? Choose the correct answer below. 0 A. The power is zero att=11 and t=23 hr. 0 B. The power is zero att= 5 and t= 17 hr. 0 C. The power is zero att= 8 hr. 0 D. The power is zero att=20 hr. 6. At what time(s) on the interval [0.25] is the power at its maximum? Choose the correct answer below. 0 A. The power reaches its maximum at times t= 11 and t= 23 hr. 0 B. The power reaches its maximum at t = 15 hr. 0 c. The power reaches its maximum at timest= 5 and t= 17 hr. 0 D. The power reaches its maximum at t = 23 hr