Derivative1. Let 34)(2 xxxf. Find ).(' xf2. A dynamite blast blows a heavy rock straight up with a launch velocity of 160ft/sec. Itreaches a height 216160)( ttts feet after t seconds.(a) Find the average speed of the rock during the first 2 seconds after launch.(b) How fast is the rock going when it is 256ft above the ground?3. Suppose the cost, C, in thousands of dollars, of a jacket manufacturer is given by 226)( xxC , where x is the number of jackets produced in thousands.(c) Find the average rate of change of the cost as the production-level increases from 4000 to 4100 jackets.(d) Find the instantaneous rate of change of the cost when x = 4.[NOTE: The instantaneous rate of change of the cost is called Marginal Cost]4. The revenue, R, in hundreds of dollars, for a kitchen sink manufacturer is given by 201.010)( xxxR , where x is the number of sinks sold.(a) Find the average rate of change of the revenue as the sale-level increases from 100 to 110 sinks.(b) Find the instantaneous rate of change of the revenue when x = 100.[NOTE: The instantaneous rate of change of the revenue is called Marginal Revenue]5. The profit, P, in millions of dollars, of a truck manufacturer is given by is given by LIMIT DEFINITION:hxfhxfxfh)()(lim)('01610)(2 xxxP, where x is the number of trucks sold in thousands.(a) Find the average rate of change of the profit as the sale-level increases from 1000 to 1100 trucks.(b) Find the instantaneous rate of change of the profit when x = 1000.[NOTE: The instantaneous rate of change of the profit is called Marginal Profit]6. Let 43)(2 xxxf(a) Find the slope of the secant joining the points on the graph of f corresponding to x = 2 and x = 3(b) Find the slope of the tangent to the curve at the point corresponding to x = 2.(c) Find the equation of the tangent to the curve at the point corresponding to x =
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