m =210h10+x10F(0m10)2 装 红∈(-o,-1),有f()>0→f(x)严格增加 装 红∈(-1,1)，有f'()<0→f(x)严格减少 红∈(1，+o∞)，有f()>0→f(x)严格增加 订 线 -框大美程-1+31-8秀板大出1果板小感 内 答 题 无 效 数学分析四试题第5页（共8页）❈ ➽ ❶ ❙ ❽ ❑ ➹ ✟ ** ** ** ** ** ** ** ** ** ** ❈ ** ** ** ** ** ** ** ** ** ** ➽ ** ** ** ** ** ** ** ** ** ** ❶ ** ** ** ** ** ** ** ** ** 7. ➛➻ê y = f(x) = x10x ✛➌✣✓ê❺✓✣✓ê. ✮: dy dx = dx dx10x + x d10x dx = 10x + x10x ln 10 = 10x (1 + x ln 10). d 2 y dx2 = [10x (1 + x ln 10)]0 = 10x ln 10(1 + x ln 10) + 10x ln 10 = 210x ln 10 + x10x (ln 10)2 . 8. ➛➻ê f(x) = x 3 − 3x + 1 ✛î❶ü◆➠♠❺✹❾. ✮: D(f) = (−∞, +∞), f0 (x) = 3x 2 − 3 = 3(x − 1)(x + 1). ❡✲ f 0 (x) = 0, ❑ ✚✔➢➼✿ x = −1, x = 1. ❫➢➼✿ò D(f) ➞➃ (−∞, −1), (−1, 1),(1, +∞). ∀x ∈ (−∞, −1),❦ f 0 (x) > 0 =⇒ f(x) î❶❖❭ ∀x ∈ (−1, 1),❦ f 0 (x) < 0 =⇒ f(x) î❶⑦✟ ∀x ∈ (1, +∞),❦ f 0 (x) > 0 =⇒ f(x) î❶❖❭ ↕➧ x = −1 ➫✹➀✿, f(−1) = −1 + 3 + 1 = 3 ➃✹➀❾; x = 1 ➫✹✂✿, f(1) = 1 − 3 + 1 = −1 ➫✹✂❾. ê➷➞Û(I)➪❑ ✶ 5 ➄↔✁ 8 ➄↕