please answer ALL QUESTIONS:

Math 172 Applications review worksheet Name: Note that this is NOT a sample final exam! 1. Suppose that f has values given by the following: -99 999 1.001 1.01 f(x) -2.9604 -2.9960 -3.0000 -3.0040 -3.0404 Estimate the value of f'(1) as closely as you can using the table. 2. Suppose that g(t) - (t + 4)2 + 2t + 7. (a) Find g'(t) from the definition, that is, using difference quotients and limits. (b) Find the slope of the tangent line to y - g(t) at t - 5. (c) Find the equation of the tangent line to y - g(t) at t - 5. 3. Suppose that the position of a particle is given by the graph below. (a) Describe in words the motion of the particle - moving forward? Backward? Slowing down? Speeding up? (b) On the same axes, or on different axes with the scales clearly labeled, sketch the velocity and acceleration of the particle. 4. Suppose that a toy car has position function s(t) - 2 cos(3t + 1), where t is measured in seconds and distance is measured in meters. (a) How fast is the car traveling at t - 10 seconds? (b) Find the velocity and acceleration functions for the toy car. 5. Find the tangent line to y - tan() at a - x/6. 6. Suppose that it takes about 12 hours to drain a storage tank by opening the valve on the bottom. The depth y of fluid in the tank & hours after the valve is opened is given by the formula y - 6 (1 -12) where y is measured in meters. Find the rate at which the water level is falling at time f. When is the fluid level falling fastest? Slowest? What is the rate at which the water level is falling at these times? 7. Suppose that we have the curve a ty' - 9ry - 0. (a) Find the slope of this curve at the point (z, y). (b) Find the equation of the tangent line to the curve at the point (2, 4). 8. Suppose that the functions f(x) and g(x) and their derivatives have the following values at T - 0 and x - 1. I f(x) g(x) f'(a) g(a) 0 -3 1/2 3 5 1/2 (a) Find (f - g?)'(0).(b) Find (fog)'(0) (c) Find (f/(g + 1))'(1) 9. Use a tangent line approximation to approximate (1.0002)50. How about (.9998)507 10. Find and classify the critical points of f(x) - 2x - 32/3 and find any inflection points. 11. Find and classify the critical points of f(x) - (1 + e ?) and find any inflection points. 12. Find the global maxima and global minima of f(x) - 2 + In(x) for .5