Sketch the graphs of the functions f and g. f(x) = −x2 + 2x + 2,    g(x) = −x + 2     Find the area of the region enclosed by these graphs and the vertical lines  x = 0  and  x = 3.        square units

Find the intercepts of the function. f(x) = x4 − 625   x-intercept      (x, y)  =                 (smaller x-value) x-intercept      (x, y)  =                 (larger x-value) y-intercept      (x, y)  =

Answer: A carpenter wants to make a rectangular bookcase like the one shown here. It should have a horizontal top, bottom, and middle shelf, and vertical back and two sides. The depth of the bookcase must be 1 ft, and its total volume must be 12 ft. a. Express the total surface area of the bookcase as a function of its height. Answer: b. What height and width of the bookcase will minimize its total surface area?

Find the interval in which the function given by h(x)= 4x – 6x – 72x + 30 is decreasing.