Test _1 Review Sheet_1

Test _1 Review Sheet_1 - Test #1 Review Sheet Directions:...

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Directions: For all problems round to the nearest thousandths as necessary. 1. A town’s population P is a function of time P=f(t) where t=years since 1970. Interpret f(3)=25,000 and f’(3)= 2000. If f”(3) is negative, what does that tell us about the population growth rate. 2. f(x)=4x+2, g(x)=5x-1, and h(x)=5-x. Find: a. f(2) b. g(2) c. f(g(2)) d. ( ) fgh 2 e. ( ) fgh x 3. In the graph a the right, the marks the origin. a. Find f(-1) b. ESTIMATE f’(2) c. Is the first derivative always positive? negative? neither? d. How about the 2 nd derivative? e. Is the graph concave up or down? 4. Your grade in this class on this test is a function of the number of hours you spend studying. G=f(t) where t= number of hours studying and G is percentage grade. a. Interpret f(0)=35 and f(8)=95. b. If you graphed this function would you anticipate the first derivative to be positive or negative? c. What are the units of the first derivative? d. If you graphed this function would you anticipate the 2 nd derivative to be positive or negative? x f(x) 2 7 5 9 8 11 11 13 5. Find the equation of a line if we know… a. it’s slope is 2 and it goes thru the point (0,-5) b. it goes thru (-8,4) and (-3,2) 6. Using Chart 1 at the right, find each: a. f(5) b. equation of the line represented. c. “bonus” points if you can find f’(x) and f”(x). Chart 1 7. A taxi company charges $2 plus 40 cents per mile find the charge (c) the company charges a customer to go m miles. x f(x) 1 30 2 50 3 58 4 62 8. Chart 2 depicts the height (ft) a t-shirt reaches when fired by Cocky from a t-shirt cannon. Assume that the height it reaches is a function of the number of seconds t after it was fired- H=f(t) a. Find f(3) and explain its meaning. b.
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Test _1 Review Sheet_1 - Test #1 Review Sheet Directions:...

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