Thinkwell | 201 Test 2: Chapters 3 Derivatives and 4 Computations Find the derivative. Of' ( 2 ) = 24+23 +12 + 1 f (x) = (2+1) (22+1) 70 f'(x) =3x2 +2x +1 I latewad of'(x) =13+x2+x+1 of' (2) = 4x3 + 3x2 + 2x +1 5 ) Let f'(x) = 3x2 + 4x define the instanta- 10 ft / min neous rate of change (in ft/min) of a car 6 7 ft /min moving along the r-axis. What is the 3 ft / min instantaneous rate of change at time 1 min? 4 ft / min Find the derivative. Of' (2) = (12 + 1) (2x) f (2) = (22 + 1)2 Of' (x ) = 2 (12 + 1 ) Of' (2 ) = 2 (22 + 1 ) ( 2x ) Of' (x) = 2x Suppose you are given a function f(x) and you I only are told that f'(a) exists. What do you know III only about the function f(x)? II and III I, II, and III I. The slope of the line tangent to f(x) is positive. II. The instantaneous rate of f(x) at a is negative. III. The function is defined at f(a). B ) This limit represents the derivative of some f (z) = VI function f at some number a. f ( 20 ) = 2 V2 + 4x - V2 lim Of(x) = Ar-0 4x What is f()? Of(x) = V2 9 ) The position of a car at time t is given by the function p(1) = -4 2 + 41 -17. Where will the car be when it moves at a 04 velocity of 10? Assume t 2 0. 3 - 3