.. Show all your workings here. 4Sample

1. Consider the functions f and g with the information in the table. 2 f(x) f(I) 3 g(x) -2 g (x) 0 -1 A) If a(z) = f(g(z)), then calculate a' (4). B) If b(x) = 9(f(x)), then calculate b'(0). C) If e(r) = f(f(x)), then calculate c(1). D) If p(x) = g(r?), then calculate p'(0). E) If q(r) = In(f(r)), then calculate d'(2). F) If r(x) = g(tan r), then calculate r'(-). G) If s(x) = vf(4r), then calculate s'(1). 2. Consider the curve defined by the equation y? = -x3 + 3x3 + 2. A) Find the equation of the line tangent to the curve at the point (1, 2). B) At what point(s) is the line tangent to the curve horizontal? 3. A circle is expanding and the area of the circle is 4x cm- and is growing by 5 cm-/min, how quickly is the radius changing? 4. The power (in watts) provided by a circuit is given by the formula P = R/?, where R is the resistance (in ohms) and / is the current (in amps). The resistance is currently 100 ohms and decreasing at a rate of 5 ohms per minute, and the power is staying constant. If the current is 3 amps, then how is the current changing? 5. Person A is starting at the origin, and person B is starting 5 meters east. If person A is walking north at a constant rate of 3 meters/minute and person B is walking south at a constant rate of 4 meters/minute, how quickly is the distance between the people changing 4 minutes after they start walking? 6. A water cup in the shape of an inverted cone has a radius of 4 cm and a height of 12 cm. Water is leaking out at a rate of 3 cm*/sec. How fast is the water level changing when the depth is 6 cm? (Recall that the volume of a cone is given by V = - Be sure to include units.7. A 20 foot long ladder leans against a vertical wall when the bottom of the ladder begins to slide away from the wall. If the bottom of the ladder is sliding along the floor at a rate of 2 ft/s when it is 12 feet from the wall, how fast is the top of the ladder sliding down at that instant? 8. If f(x) = (cosz), find f'(1). 9. If g(x) - Ves + 1(x] + 2)3 (3r + 5)4 -, find g'(1). 10. if h(x) = 5(0.3)", find value(s) of a for which h'(z) = -3. 11. Find the equation of the tangent line to y = arcsin(3x) at the point with a = 1/6