By Warren B. Gordon
Utilized Calculus for enterprise, Economics, and Finance is a mix of the authors' prior texts Precalculus and parts of Calculus and utilized Calculus. This unmarried textual content can be utilized to hide the content material of an utilized calculus path for non-science majors. carrying on with the procedure utilized in its precursor texts, utilized Calculus for enterprise, Economics, and Finance good points the combination of precalculus with the calculus in addition to the mixing of expertise with either matters.
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Extra info for Applied Calculus For Business, Economics, And Finance
649 Since x represents a length, it must be a positive number, therefore, we reject the negative solution. 649 inches. Exercise 7 (a) If the profit P (in dollars) earned by selling x units of some item is given by the equation P = -3x2 + 200x - 2000, find (to the nearest integer) the value of x which produces a profit of $1,000. (b) Find the quantity (to the nearest integer) which produces a break even situation 1Profit = 02. Solution (a) We need to solve the equation -3x 2 + 200x - 2000 = 1000 or equivalently 3x2 - 200x + 3000 = 0 We may solve this equation using the quadratic formula.
1 The Line Finally, we factor the m from both terms on the right hand side of the equation, to get y - y1 = m1x - x12. This is the so-called point-slope equation of a straight line. The Point-Slope Equation of a Line If you are given the slope of a line m, and know the coordinates of one point 1x1, y12 on the line then you may determine an equation for the line by simply substituting the information into the point-slope equation y + y1 * m1x + x 12 Of the various forms of the equation of the straight line, the Point-Slope form is the most useful for calculus.
Consider the following examples. Example 5 The altitude h of a rocket fired vertically upward is given by the equation h = -16t2 + 2500t, where t is the time from firing in seconds. (a) How long does it take the rocket to reach an altitude of 4700 feet? (b) How long does it take for the rocket to return to the ground? Solution (a) We are asked to find t when h = 4700 feet. 903 seconds. Why are there two solutions? 903 seconds. However, this rocket will achieve its maximum altitude and then begin to come down.