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受欢迎的函数 >

值域 f(x)=(5x-2)^2(3x+4)^3(x+1)^5

解答

值域

f (x) = (5 x - 2)^{2} (3 x + 4)^{3} (x + 1)^{5}

解答

f (x) \geq \frac{- 2.1127 E 13 - 4794026762 38689 + \frac{1.7017 E 14 + 863964681454 38689}{30} + \frac{- 3.09221 E 16 - 1.57226 E 14 38689}{2250} + \frac{1.19014 E 25}{30 0 ^{5}} + \frac{5.62346 E 18 + 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( - 167 - 38689 )}{15} + \frac{64 ( 33289 + 167 38689 )}{1125} + \frac{4737696424 + 24314072 38689}{253125} + \frac{- 16 7 ^{5} \cdot 60529 - 16 7 ^{5} \cdot 287 38689 - 3868 9 ^{2} \cdot 61645458 - 1.85497 E 15 38689 - 2.7206 E 17}{6.83438 E 13} - \frac{703441550854 + 3576438362 38689}{18984375} + \frac{3868 9 ^{2} \cdot 60529 + 5202827029232 38689 + 9.32772 E 14}{45562500000} + 256

+1

间隔符号

[\frac{- 2.1127 E 13 - 4794026762 38689 + \frac{1.7017 E 14 + 863964681454 38689}{30} + \frac{- 3.09221 E 16 - 1.57226 E 14 38689}{2250} + \frac{1.19014 E 25}{30 0 ^{5}} + \frac{5.62346 E 18 + 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( - 167 - 38689 )}{15} + \frac{64 ( 33289 + 167 38689 )}{1125} + \frac{4737696424 + 24314072 38689}{253125} + \frac{- 16 7 ^{5} 60529 - 16 7 ^{5} 287 38689 - 3868 9 ^{2} 61645458 - 1.85497 E 15 38689 - 2.7206 E 17}{6.83438 E 13} - \frac{703441550854 + 3576438362 38689}{18984375} + \frac{3868 9 ^{2} 60529 + 5202827029232 38689 + 9.32772 E 14}{45562500000} + 256, \infty)

求解步骤

确定每个定义区间的极小值和极大值并将结果合并

(5 x - 2)^{2} (3 x + 4)^{3} (x + 1)^{5}

的定义域

: - \infty < x < \infty

(5 x - 2)^{2} (3 x + 4)^{3} (x + 1)^{5}

的极值点:

鞍点

(- \frac{4}{3}, 0),

极小值

(\frac{- 167 - 38689}{300}, \frac{- 2.1127 E 13 - 4794026762 38689 + \frac{1.7017 E 14 + 863964681454 38689}{30} + \frac{- 3.09221 E 16 - 1.57226 E 14 38689}{2250} + \frac{1.19014 E 25}{30 0 ^{5}} + \frac{5.62346 E 18 + 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( - 167 - 38689 )}{15} + \frac{64 ( 33289 + 167 38689 )}{1125} + \frac{4737696424 + 24314072 38689}{253125} + \frac{- 16 7 ^{5} \cdot 60529 - 16 7 ^{5} \cdot 287 38689 - 3868 9 ^{2} \cdot 61645458 - 1.85497 E 15 38689 - 2.7206 E 17}{6.83438 E 13} - \frac{703441550854 + 3576438362 38689}{18984375} + \frac{3868 9 ^{2} \cdot 60529 + 5202827029232 38689 + 9.32772 E 14}{45562500000} + 256),

鞍点

(- 1, 0),

极大值

(\frac{- 167 + 38689}{300}, \frac{4794026762 38689 - \frac{2.34728 E 17}{253125} + \frac{1.7017 E 14 - 863964681454 38689}{30} + \frac{1.57226 E 14 38689 - 3.09221 E 16}{2250} + \frac{3.61021 E 17}{30 0 ^{5}} + \frac{5.62346 E 18 - 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( 38689 - 167 )}{15} + \frac{64 ( 33289 - 167 38689 )}{1125} + \frac{4737696424 - 24314072 38689}{253125} + \frac{16 7 ^{5} \cdot 287 38689 + 1.85497 E 15 38689 - 16 7 ^{5} \cdot 60529 - 3868 9 ^{2} \cdot 50541715 - 2.88681 E 17}{6.83438 E 13} + \frac{3576438362 38689 - 703441550854}{18984375} + \frac{3868 9 ^{2} \cdot 60529 + 9.32772 E 14 - 5202827029232 38689}{45562500000} + 256),

极小值

(\frac{2}{5}, 0)

确定

- \infty < x < \infty

区间对应的值域:

\frac{- 2.1127 E 13 - 4794026762 38689 + \frac{1.7017 E 14 + 863964681454 38689}{30} + \frac{- 3.09221 E 16 - 1.57226 E 14 38689}{2250} + \frac{1.19014 E 25}{30 0 ^{5}} + \frac{5.62346 E 18 + 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( - 167 - 38689 )}{15} + \frac{64 ( 33289 + 167 38689 )}{1125} + \frac{4737696424 + 24314072 38689}{253125} + \frac{- 16 7 ^{5} \cdot 60529 - 16 7 ^{5} \cdot 287 38689 - 3868 9 ^{2} \cdot 61645458 - 1.85497 E 15 38689 - 2.7206 E 17}{6.83438 E 13} - \frac{703441550854 + 3576438362 38689}{18984375} + \frac{3868 9 ^{2} \cdot 60529 + 5202827029232 38689 + 9.32772 E 14}{45562500000} + 256 \leq f (x) < \infty

将所有定义域区间对应的值域合并得出函数值域

f (x) \geq \frac{- 2.1127 E 13 - 4794026762 38689 + \frac{1.7017 E 14 + 863964681454 38689}{30} + \frac{- 3.09221 E 16 - 1.57226 E 14 38689}{2250} + \frac{1.19014 E 25}{30 0 ^{5}} + \frac{5.62346 E 18 + 2.85894 E 16 38689}{337500}}{450000000} + \frac{64 ( - 167 - 38689 )}{15} + \frac{64 ( 33289 + 167 38689 )}{1125} + \frac{4737696424 + 24314072 38689}{253125} + \frac{- 16 7 ^{5} \cdot 60529 - 16 7 ^{5} \cdot 287 38689 - 3868 9 ^{2} \cdot 61645458 - 1.85497 E 15 38689 - 2.7206 E 17}{6.83438 E 13} - \frac{703441550854 + 3576438362 38689}{18984375} + \frac{3868 9 ^{2} \cdot 60529 + 5202827029232 38689 + 9.32772 E 14}{45562500000} + 256

作图

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