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The august 31, 2006 math 106 exam focusing on derivatives and rates of change. The exam includes finding derivative formulas, calculating changes and average rates of change, translating equations, and using limit definitions. Questions cover various functions such as quadratic, logarithmic, and polynomial.
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Math 106 August 31, 2006
Name
You must show all your work. Partial credit will be given.
(a) g(x) = − 3 x^2 + 5x − 2 x−^4.
(b) y =
2 x^2 − 2 x^2
(c) f (x) = 2x^2 + 3 ln x.
(d) y = (3x^3 + 15x − x−^1 )^6.
(e) f (x) =
(2x^2 − x)^5
(f) y = (ln (x))e^3 x.
(g) y = 12x + x 3
3 x + 2.
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(a) Estimate the average rate of change in Slim’s average monthly profit if the number of cars he sells increases from 40 to 160 cars. (6 pts)
(b) Estimate the rate of change for average monthly profit when 140 cars are sold. (6 pts)
