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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 0

X Intercepts : (\frac{3}{2}, 0), Y Intercepts : (0, 81)

Asymptotes : None

Extreme Points : Minimum (\frac{3 - 58}{14}, \frac{17719364 58 - 139804449}{470596} + \frac{1001146165 + 1133380 58}{11529602} + \frac{10 9 ^{5} \cdot 55273 + 10 9 ^{5} \cdot 6876 58 + 9.12406 E 14 - 3.39424 E 14 58}{1.73625 E 14} + \frac{3.48346 E 13 - 4325237175620 58}{885842380864} + \frac{107810211185 - 19899384880 58}{2259801992} + \frac{405 ( 109 - 20 58 )}{196} + 81), Maximum (\frac{3 + 58}{14}, \frac{- 139804449 - 17719364 58}{470596} + \frac{1001146165 - 1133380 58}{11529602} + \frac{10 9 ^{5} \cdot 55273 + 3.39424 E 14 58 + 9.12406 E 14 - 10 9 ^{5} \cdot 6876 58}{1.73625 E 14} + \frac{3.48346 E 13 + 4325237175620 58}{885842380864} + \frac{107810211185 + 19899384880 58}{2259801992} + \frac{405 ( 109 + 20 58 )}{196} + 81), Minimum (\frac{3}{2}, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

(2 x - 3)^{4} (x^{2} + x + 1)^{5} : - \infty < x < \infty

Range of

(2 x - 3)^{4} (x^{2} + x + 1)^{5} : f (x) \geq 0

Axis interception points of

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

X Intercepts

: (\frac{3}{2}, 0),

Y Intercepts

: (0, 81)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(\frac{3 - 58}{14}, \frac{17719364 58 - 139804449}{470596} + \frac{1001146165 + 1133380 58}{11529602} + \frac{10 9 ^{5} \cdot 55273 + 10 9 ^{5} \cdot 6876 58 + 9.12406 E 14 - 3.39424 E 14 58}{1.73625 E 14} + \frac{3.48346 E 13 - 4325237175620 58}{885842380864} + \frac{107810211185 - 19899384880 58}{2259801992} + \frac{405 ( 109 - 20 58 )}{196} + 81),

Maximum

(\frac{3 + 58}{14}, \frac{- 139804449 - 17719364 58}{470596} + \frac{1001146165 - 1133380 58}{11529602} + \frac{10 9 ^{5} \cdot 55273 + 3.39424 E 14 58 + 9.12406 E 14 - 10 9 ^{5} \cdot 6876 58}{1.73625 E 14} + \frac{3.48346 E 13 + 4325237175620 58}{885842380864} + \frac{107810211185 + 19899384880 58}{2259801992} + \frac{405 ( 109 + 20 58 )}{196} + 81),

Minimum

(\frac{3}{2}, 0)

Graph

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Frequently Asked Questions (FAQ)

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