# 1325-pt3 - Exam Name Find the open interval(s where the...

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Exam Name___________________________________ Find the open interval(s) where the function is changing as requested. 1) Decreasing; f(x) = - x + 3 2) Decreasing; f(x) = x + 4 x - 6 3) Increasing; y = 7x - 5 4) Increasing; f(x) = .25x 2 - .5x 5) Increasing; f(x) = x 2 - 2x + 1 6) Increasing; y = x 2 + 2 7) Decreasing; f(x) = x 3 - 4x 8) Increasing; y = x 4 - 18x 2 + 81 9) Increasing; f(x) = 1 x 2 + 1 Identify the intervals where the function is changing as requested. 10) Decreasing 11) Decreasing 1

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12) Decreasing 13) Decreasing Solve the problem. 14) The number of people P(t) (in hundreds) infected t days after an epidemic begins is approximated by P(t) = 9 - 35t - 5 2 t 2 . When will the number of people infected start to decline? Find the values of any relative extrema. 15) f(x) = x 2 + 1 x 2 16) f(x) = x 3 - 12x + 2 17) f(x) = 2 + 8x - x 2 18) f(x) = x 2/5 - 1 19) f(x) = 1 x 2 + 1 20) f(x) = 1 x 2 - 1 21) f(x) = x 2 + 2x - 3 22) f(x) = x 3 - 3x 2 + 1 23) f(x) = x 4/3 - x 2/3 24) f(x) = 3x 4 + 16x 3 + 24x 2 + 32 2
Find all relative maxima or minima. 25) y = x + ln uni2223 x uni2223 26) y = (ln 3x) 2 , x > 0 27) y = xe 8x 28) y = x ln uni2223 x uni2223 , x > 0 29) f(x) = x 4 8lnx 30) y = 2xe - x 31) f(x) = x 3 e x - 6 32) y = (ln x) 2 , x > 0 33) y = ln x - x, x > 0 Use the derivative to find the vertex of the parabola. 34) y = - 3x 2 - 12x + 4 35) y = 2x 2 + 20x + 10 Solve the problem. 36) An architect needs to design a rectangular room with an area of 74 ft 2 . What dimensions should he use in order to minimize the perimeter? 37) Find the dimensions that produce the maximum floor area for a one - story house that is rectangular in shape and has a perimeter of 131 ft.

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