# Find all values of x if any where the tangent line to the...

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Math C140 Business Calculus Final Review (Chapters R. 1-6.3) 45 Questions The Exam is NOT Multiple-Choice; Show Your Work for Partial Credit One Page of Notes Allowed (NO PROBLEMS, Formulas Only) and a Calculator (Any Type) is Allowed Turn in Your Page of Notes with Exam Evaluate the function. 1) For f(x) = x2 + 5 X / find &*J&zM. h Graph the function and then find the specified limit. When necessary, state that the limit does not exist. 3)f(x) = p-x, for x s 2. K m f ( x ) 11 + 2x, for x > 2. x _ » 2 + to--y 6-- ( I I I I I I I I I I I I I I I I I I I I > • 10 <S ' -4 -2 ' • • 2 ' 4 • 6 -'6-- - re- Find the derivative. „ . 4 3 9
Find all values of x (if any) where the tangent line to the graph of the function is horizontal. 5 ) y = x 3 + 4 x 2 - H x + l l Differentiate. 6) f(x) = (3x - 5)(2x3 - x 2 + 1) 7) g(x): X 2 x - 11 8) f (x) = (2x2 + 2 ) 3 9) f(x)=-s/l - 18x F i n d ^ . dx2 10) y = 2x4 - 6 X 2 + 6 Determine where the given function is increasing and where it is decreasing. 11) f(x) = x3 - 12x + 2 Determine where the given function is concave up and where it is concave down. 12) f(x) = x4 - 24x2 Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line «). 13) f(x) = x + -^-; [-7,-1] 14) f(x) = x3 - 6x2 + 8; (0, ») Solve the problem. 15) The total-revenue and total-cost functions for producing x clocks are R(x) = 480x - 0.01x2 a n d C(x) = 200x + 100,000, where 0 < x < 25,000. What is the maximum annual profit? 16) A company estimates that the daily cost (in dollars) of producing x chocolate bars is given by C(x) = 1410 + 0.04x + 0.0002x2. Currently, the company produces 690 chocolate bars per day. Use marginal cost to estimate the increase in the daily cost if one additional chocolate bar is produced per day. 17) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? 2
Differentiate.
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