Part 1

d) j(ze) = (25 . 27 )4 j'(x) = e) m(x) = V1 + eVitr' m'(x) = f) Solve part (d) without using the Chain Rule . j' (z) =(1 point) At time t, in seconds, the position, in meters, of a particle moving along the x-axis is a (t) = to - 3t. Assume for all parts of this problem that t 2 0. a) Find the particle's acceleration whenever the velocity is zero. Acceleration when velocity is zero: b) Find the velocity of the particle whenever the acceleration is zero. Velocity when acceleration is zero:1 int] For what interval is the function f 1: = 2333 concave dam { PD Interval: EEE ' (1 point) Ash population is approximated by P(t) = 126\"\" (sin(%t) + 3) , where t is in months. Calculate the following. a) P(12) = _ 6) 13112) = _ a (3) Based on the answers to parts a) and b) above, we may conclude that the sh population was EEE -_ sh after one year. We may also conclude that the sh population was ? v _ by :E sh per ? v . (1 point) Consider the values f(4) = 3 f'(4) =9 f"(4) = 2 g(4) = 3 g'(4) =9 g"(4) =4 f(g(4)) = 6 f'(g(4)) =1 f"(g(4)) = 3 Using the above values, evaluate the following: a) d2 dr2 If(x)g(x) at x = 4: b) d2 dx2 If(g(ze) )] at x = 4:[1 paint} Let f(s:) he a function such that f'{3} = 3. a) What is the derivative of f (51:) when ::: = 0.6? Answer: ::: b) What is the derivative at Hz: 3] when :1: = ? Answer: e} what is the derivative of f (g) when :1: = 13? Answer: (1 point) Using the table below, evaluate the following quantities. 0 1 2 3 4 5 f(ac) 4 1 4 4 4 f' (z) 5 2 5 1 4 3 2 4 1 2 g'(x) 5 3 4 2 1 5 a) h'(2), where h(x) = f(g(x)) h' ( 2) = b) h'( 4), where h(x) = g(f(x) ) h' ( 4) = c) h'(1), where h(ze) = g(g(x)) h'(1) = d) h'(2), where h(x) = (f(g(x)))2 h' ( 2 ) = e) h'(5), where h(x) = Vg(f(x)) + 3 h'(5) = f) h'(2), where h(x) = f(x)g(z) (1242) 2 h'(2) = g) h'(2), where h(ze) = f(2) g(12) h'(2) = h) h'(1), where h(x) = (9(x)) 3 h' (1) =