Hi, I need help with Calculus, take your time, thank you

Below are the graphs of 6 functions A-F. There are also graphs of 5 derivative functions 1-5. Match each function with it's derivative. One derivative is missing! Try sketching it yourself before looking at the answer. Consider the function defined by P (a) = f(x) g(x) Use the given graphs to find the value of P' (2) . 5 g (x ) -3- 0 2\fConsider the function h (3:) : 3f (3:) + 3:29 (3:) where f (3:) and g (3:) are differentiable functions. Use the information in the table to nd the value of h' (4) . 3: 0 2 4 6 f (3:) -1 -6 -2 0 f' (3:) 8 1 -4 5 gr (3:) 15 -3 3 6 012 052 0-44 018 086 024 For what values of a does the function f (x ) = 12x - x have a horizontal tangent line? Select all that apply. 0 0 0 1 O 12 0 -1 0 4 0 3 0 2 0 -3 0 -4 0 -2 O -12Consider the function f (:12) = (1:33 + bar where a, and b are constants. Suppose f' (1) = 12 and fJr (0) = 6 . What are the values of a and b ? Suppose P (t) represents the size of a population at time t. What do each of the following quanties represent? [Select ] ' the instantaneous rate of change in population at time t=1 the total change in population from t=1 to t=4 the instantaneous rate of change in population at time t=4 the average rate of change in population over the interval [1,4] Suppose P (t) represents the size of a population at time 1?. What do each of the following quanties represent? a} w ' [Select] v b)P(3+h)P(3) l [Select] v C) 19(5) + P! (5) h L the average rate of change in the time from t=3+h to t=3 the average rate of change in the time from t=3 to t=3+h d} P(al0.1)P(a) ' [Sell 0.1 the total change in the time from t=3+h to t=3 the instantaneous rate of change at time t=3 the total population change in the time from t=3 to t=3+h aw ' [Select] v' b)p(3+h)_p(3) ' [Select] v' c) P(5) + P" (5) h ' [Select] V an approximation to the value P(h) an approximation to the value P(5+h) an approximation to the value P(S) the instantaneous rate of change in population at time t=5 the average rate of change in population from time t=h to t=5 d} W [ Select] v 0.1 the total change in population in the time from t=a to t=a+O.1 the instantaneous rate of change in population at time t=a the instantaneous rate of change in population at time t=a+0.1 Question 2 _ . . . the average rate of change In population In the time from t=a to t=a+0.1 Read Example 3.36 in the textbook 2'. Suppose the position of a train travelling along a straight track is given by s (t) : t3 6132 + 1% where t Z 0. At what time is the train standing still? (Answer with just a numerical answer e.g. 5, rather than "At t=5".) Functions A-F: Function A Function B Function CRead Example 3.38 in the textbook :2. A company sells umbrellas. Suppose that the number, 3:, of umbrellas that are sold per week is related to the price, p (in dollars}, that is charged, according to the equation: p(:1:) : 25 0.53: where 0 g :1: g 50 a} Find the marginal revenue when a: : 20. [ Select] v MR(20] = 5 rt (a) represent? MR(20) = 15 MR(20) = 25 MR(20] = 3 ' MR(20] = 20 ' A company sells umbrellas. Suppose that the number, a, of umbrellas that are sold per week is related to the price, p (in dollars), that is charged, according to the equation: p (ac) = 25 - 0.5x where 0