6. Let k(x) = Use the fact that k'(x) = 50x and k"(x)= - 50 (3x²-16) to answer the following %3D 2+16* about the graphy = k(x). 6.1. Find any x-intercepts. 6.2. Find any asymptotes, either vertical or horizontal. 6.3. Determine any local maximum and local minimum points. Be sure to say which each is and give reasons.

8. The Federal debt held by the public as a percent of the gross domestic product (GDP) is modeled by the function y = 0.00630t3 – 0.289t² + 4.00t + 25.3 where t is the time (in years) since 1980. Find the average public debt as a percent of GDP, from 2000 to 2015.

8. Identify any asymptotes, extrema, points of inflection and/or intercepts for (x² – 7x+13) = (x)f (x-4) %3D bisce

The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)