(a) 令f(x) = x⁵ + 2x³ + 2x, 且 f^-1(x) 代表 f(x) 之反函數, 求 (f^-1)'(-5)。

3. Find the integraldA , where R is the trapezoidal region with vertices (1, 0), (2, 0), (0, −2), and (0, −1).

V. Composition (30%)Write a 300-word essay on how to enjoy doing nothing.

IV. Composition writing: 30%The 85 richest people on Earth... are a small part of the richest 1% of the population, which combined owns about 46% of global wealth, according to the report from British humanitarian group Oxfam International.(from Los Angeles Times, January 20, 2014)Based on the given report, please write a paragraph of 300 words to discuss the problem of income inequality in Taiwan and offer your suggestion(s) to improve this situation in Taiwan.

1. (10%) 考慮以「o」表示「是」、「×」表示「否」,填入下表:

(b) 已知2y2 = 28 - x2 + xy, 求在 (x,y) = (-2,-4) 之值。

(c) 求積分dx。

(d) 求積分∫x cos x dx.

(a) 畫出函數f(x)之圖形。

(b) 求 F(x)之臨界點 (critical point), 及說明在每一臨界點上函數 F(x)是否有局部極大值、局部極小值、反曲點 (local maximum、local minimum、inflection point)。

(c) 求出F(x) 在x=2時的切線。