A 10-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 3 feet per second. How fast is the top of the ladder sliding down the wall when the bottom is 6 feet from the wall? . . . The ladder is sliding down the wall at a rate of ft/sec. (Type an integer or a simplified fraction.)Suppose that for a company manufacturing calculators, the cost, revenue, and prot equations are given by 2 X C=80,000+40X, R=200xE, P=RC where the production output in 1 week is x calculators. If production is increasing at a rate of 400 calculators per week when production output is 6,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. A) Costs are |:| at the rate of $|:| per week at this production level. (Simplify your answer.) \fFind f'(x) and nd the equation of the line tangent to the graph of f at the indicated value of x. f(x)=x(4 -x)2; x=2