數學題目微積分(急)

1.y = 4x^6 – 3x^5 -10x^2 + 5x + 16y’ = 24x^5 – 15x^4 – 20x + 5 2.y = √x – 6(√x)^(1/3)y’ = (1/2)x^(-1/2) – 6(1/3)x^(-2/3)y’ = 1/(2√x) – 2/(√x^2)^(1/3) 3.y = (3x^2 – 5)(2x^4 – x)y’ = (3x^2 – 5)’(2x^4 – x) + (3x^2 – 5)(2x^4 – x)’y’ = 6x(2x^4 – x) + (3x^2 – 5)(8x^3 – 1)y’ = 36x^5 – 40x^3 – 9x^2 + 5 4.y = (4 + 2x^2)^7y’ = 7(4 + 2x^2)^6 (4 + 2x^2)’y’ = 28x(4 + 2x^2)^6 5.y = (3x -5)/(x^2 + 7)y’ = ((3x -5)’(x^2 + 7) - (3x -5)(x^2 + 7)’)/ (x^2 + 7)^2y’ = (3(x^2 + 7) – 2x(3x -5))/ (x^2 + 7)^2y’ = (-3x^2 + 10x + 21) / (x^2 + 7)^2 6.f(x) = x^2f’(x) = lim△x→0 ((x + △x)^2 - x^2)/(△x)f’(x) = lim△x→0 (((△x)^2 + 2x△x + x^2– x^2)/(△x)f’(x) = lim△x→0 (((△x)^2 + 2x△x )/(△x)f’(x) = lim△x→0 △x + 2xf’(x) = 2x 7.f(x) = x^3/3 – x^2 -3x + 4f’(x) = x^2 -2x -3 = 0, x = 3, -1f’’(x) = 2x -2 = 0, x = 1, 反曲點(1, 1/3)f’’(3) = 4 > 0, 極低點(3, -5)f’’(-1) = -4 < 0, 極高點(-1, 17/3) 8.P(1,2), 直線 y – 2 = m(x – 1), m < 0直線x軸交點B((m-2)/m, 0), y軸交點A(0, -m+2)三角形面積 = f(m) = ((m-2)/m)( -m+2)/2f(m) = (-m^2 + 4m -4)/(2m)f’(m) = (-2m + 4)m – (-m^2 + 4m -4))/(2m^2) = 0, m = -2, 2(X) 兩交點A(0, 4), B(2, 0), 有最小面積 (-4 – 8 - 4)/(-4) = 4 9.設注水t秒, t→0杯高y = 2x注水t秒體積V = π(x^2)y/3 – π(2^2)4/3 = 2t πy^3/12 - 16π/3 = 2ty = (24t/π+ 64)^(1/3)dy/dt = (1/3)( (8t/π+ 64)^(-2/3)(24/π), t→0dy/dt = 1/(2π) 水面上升速度 = 1/(2π)

到下面的網址看看吧

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到下面的網址看看吧

▶▶http://candy5660601.pixnet.net/blog

題目在這→http://i.imgur.com/LPHuZ5c.jpg

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