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Popular >

f(x)=(2x-8)^4(x^2+x+1)^5

Solution

f (x) = (2 x - 8)^{4} (x^{2} + x + 1)^{5}

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 0

X Intercepts : (4, 0), Y Intercepts : (0, 4096)

Asymptotes : None

Extreme Points : Minimum (\frac{31 - 1857}{28}, \frac{4337139078 1857 - 187786619066}{1882384} + \frac{184 3 ^{5} \cdot 340929 1857 + 184 3 ^{5} \cdot 14949729 + 184 3 ^{3} \cdot 1.28204 E 13 1857 + 184 3 ^{3} \cdot 5.62173 E 14 - 184 3 ^{4} \cdot 142448659425 - 184 3 ^{4} \cdot 3363689025 1857 - 1857 \cdot 5.10152 E 22 - 2.09376 E 24}{39 2 ^{5} \cdot 4802} + \frac{6.34169 E 15}{39 2 ^{4} \cdot 2401} + \frac{4957912512090 - 99143668710 1857}{184473632} + \frac{184 3 ^{3} \cdot 1704645 1857 + 184 3 ^{3} \cdot 74748645 - 1.14828 E 16 1857 - 4.33084 E 17}{144627327488} + \frac{2560 ( 1843 - 45 1857 )}{49} + 4096), Maximum (\frac{31 + 1857}{28}, \frac{- 187786619066 - 4337139078 1857}{1882384} + \frac{184 3 ^{5} \cdot 14949729 + 184 3 ^{4} \cdot 3363689025 1857 + 184 3 ^{3} \cdot 5.62173 E 14 + 1857 \cdot 5.10152 E 22 - 184 3 ^{5} \cdot 340929 1857 - 184 3 ^{4} \cdot 142448659425 - 184 3 ^{3} \cdot 1.28204 E 13 1857 - 2.09376 E 24}{39 2 ^{5} \cdot 4802} + \frac{2.64077 E 20}{39 2 ^{4} \cdot 4802} + \frac{4957912512090 + 99143668710 1857}{184473632} + \frac{184 3 ^{3} \cdot 74748645 + 1.14828 E 16 1857 - 184 3 ^{3} \cdot 1704645 1857 - 4.33084 E 17}{144627327488} + \frac{2560 ( 1843 + 45 1857 )}{49} + 4096), Minimum (4, 0)

+1

Interval Notation

Domain : (- \infty, \infty)

Solution steps

Domain of

(2 x - 8)^{4} (x^{2} + x + 1)^{5} : - \infty < x < \infty

Range of

(2 x - 8)^{4} (x^{2} + x + 1)^{5} : f (x) \geq 0

Axis interception points of

(2 x - 8)^{4} (x^{2} + x + 1)^{5} :

X Intercepts

: (4, 0),

Y Intercepts

: (0, 4096)

Asymptotes of

(2 x - 8)^{4} (x^{2} + x + 1)^{5} :

None

Extreme Points of

(2 x - 8)^{4} (x^{2} + x + 1)^{5} :

Minimum

(\frac{31 - 1857}{28}, \frac{4337139078 1857 - 187786619066}{1882384} + \frac{184 3 ^{5} \cdot 340929 1857 + 184 3 ^{5} \cdot 14949729 + 184 3 ^{3} \cdot 1.28204 E 13 1857 + 184 3 ^{3} \cdot 5.62173 E 14 - 184 3 ^{4} \cdot 142448659425 - 184 3 ^{4} \cdot 3363689025 1857 - 1857 \cdot 5.10152 E 22 - 2.09376 E 24}{39 2 ^{5} \cdot 4802} + \frac{6.34169 E 15}{39 2 ^{4} \cdot 2401} + \frac{4957912512090 - 99143668710 1857}{184473632} + \frac{184 3 ^{3} \cdot 1704645 1857 + 184 3 ^{3} \cdot 74748645 - 1.14828 E 16 1857 - 4.33084 E 17}{144627327488} + \frac{2560 ( 1843 - 45 1857 )}{49} + 4096),

Maximum

(\frac{31 + 1857}{28}, \frac{- 187786619066 - 4337139078 1857}{1882384} + \frac{184 3 ^{5} \cdot 14949729 + 184 3 ^{4} \cdot 3363689025 1857 + 184 3 ^{3} \cdot 5.62173 E 14 + 1857 \cdot 5.10152 E 22 - 184 3 ^{5} \cdot 340929 1857 - 184 3 ^{4} \cdot 142448659425 - 184 3 ^{3} \cdot 1.28204 E 13 1857 - 2.09376 E 24}{39 2 ^{5} \cdot 4802} + \frac{2.64077 E 20}{39 2 ^{4} \cdot 4802} + \frac{4957912512090 + 99143668710 1857}{184473632} + \frac{184 3 ^{3} \cdot 74748645 + 1.14828 E 16 1857 - 184 3 ^{3} \cdot 1704645 1857 - 4.33084 E 17}{144627327488} + \frac{2560 ( 1843 + 45 1857 )}{49} + 4096),

Minimum

(4, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the f(x)=(2x-8)^4(x^2+x+1)^5 ?
The f(x)=(2x-8)^4(x^2+x+1)^5 is