1. "For what values of k does the graph of y=(4/3)x^3+2kx^2+5x+3 have two tangent lines parallel to the x-axis."
2. a)"Approximate the integral of x^2 dx where a=1 and b=4 using the trapezoidal rule with n=4."
b)"Find the maximum possible error in the answer to (a)."
c)"Find the numer of equal-width subdivisions required to approximate the integral with an error of less than 0.001."
3. "The base of a solid object is a circle with a radius of 4. Every verticle cross section is an equilateral triangle. What is the volume of the solid?"
4. "The base of a solid object is the region in the xy-plane bounded by the graphs of y=x^2 and y=4. Every verticle cross section parallel to the y-axis is a rectangle with a height of 3. What is the volume of the object?"
5. "The mean value theorem for integrals says that every continous function attains its average value on an interval at some point in the interval. For the function y=tanx, find some number x on the interval [(-pi/4),(pi/4)] such that f(c) equals the average calue of the function on the interval."
6. "Use differentials to estimate 4.1^4."
