math review 1

math review 1 - COMM 295 Math Review 1. Draw the following...

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Unformatted text preview: COMM 295 Math Review 1. Draw the following equation in a diagram with y on the vertical axis and x on the horizontal axis: 2x + 3y = 9. What is the vertical intercept and what is the slope? 2. Find the point of intersection of the following two lines, and then graph them: 2x + 3y = 9 x + 2y = 5 3. Find the point of intersection of the following two lines, and then graph them: x – 2y = 1 2x – 4y = ‐3 4. Graph the line: X = 5 5. Graph the line: Y = 6 6. Amy buys 10 videos each month regardless of the price. Write down the equation for Amy’s demand curve. 7. Brian cuts lawns. He faces a demand curve given by Q = 50 – 2P where Q is quantity and P is price. Write down the equation for Brian’s revenue, R, where R is a function of Q. Graph this revenue function for Q between 0 and 50. 8. A demand curve is given by Q = a – P and a supply curve is given by Q = b + 2P. Suppose that a = 100 and b = 40. What is the point where the supply and demand curves cross? Illustrate the solution in a diagram. 9. Suppose that y is a function of x. We write y = f(x). Here are some examples of such functions. c) y = 5x5 + 3x d) y = 1/x e) y = x‐2 a) y = x b) y = x2 f) y = √x g) y = 3x1/3 h) y = 3 + x1/2 i) y = ln(x) j) y = x0 The derivative of a function can be written in any of the following ways: dy/dx or df/dx or f'(x). Using dy/dx to represent the derivative, what is the derivative for each of the above functions? Draw functions a) through e) for values of x ranging from 0 to 5. Also draw the derivative for each of these 5 cases. 10. The derivative of a function is its slope. The slope is the graphical representation of a derivative. Suppose that demand is given by Q = 100 – P. Derive the revenue function R(Q). What is the derivative, dR/dQ? Illustrate R and dR/dQ on a diagram. What is the slope of R at the quantity level where R reaches its highest value? ...
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