x2 - 9 1 . Find the domain and range of the function f(x) = 4x + x . (10 points possible) 2. Using the definition of the derivative, find f (x) = if f(x) = sin x. (8 points possible)3. The table below gives values for the functions f and g and their derivatives. Identify and Justify the rule or theorem you used to nd each derivative. (9 points poseiblH points each) Find Emil)! at x = 0' Find dx a: x = 1, 4. Find the derivatives of the following functions. identify and justify the rules or theorems you used to nd each derivative. (25 points possible5 points each} a. fix) = sinth) sin(3x) b. 1+x mo=2+3ir+4tr2 c. "1 x): J; + y; (1. me) = e sin(92) e. m = W + 5ec(x)ta|1(x) 3 2 5. Consider the curve 3y -4xy+ x = 3. (6 points possible) a. d_y Find 05! . b. Write an equation for the tangent line to the curve when x = D. A 10 foot ladder is sliding down a wall (against which it is leaning) at the rate of 1 inJmin. How fast is the foot of the ladder moving away from the wall at the instant when it is 2 feet from the wall? (6 points possible) A giant spherical snowball is melting such that its radius decreases at a rate of 5 mm per hour. How fast is the surface area changing when the diameter is two meters? How fast is the VOW")? changing at that time? (10 points possible) The diagram below shows the graph of the velocity in rsec for a particle moving along the line x = 4. (10 points possible2 points each) 3. During which time interval is the particle: (i) moving upward? (ii) moving downward? (iii) at rest? b. State the acceleration of the particle at the specied times. Include units. (i) l: 0.75 (ii) t = 4.2 9. The volume of a cylinder with radius r and height h is given by V = It r h. The radius and height of the cylinder are increasing at constant rates. The radius is expanding at 1cm/3 sec and the height is increasing at 1cm/2 sec. At what rate, in cubic cm per second, is the volume of the cylinder increasing when its height is 9 cm and the radius is 4 cm? (6 points possible) 10. An airplane flies at an altitude of 5 miles toward a point directly over an observer. The speed of the plane is 600 mile per hour. Find the rates at which the angle of elevation 0 is changing when the angle is (a) 0 = 30, (b) 0 = 60, and (c) 0 = 70. (10 points possible) DO 5 mi Not drawn to scale