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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq \frac{2269 + 89 601}{8} - \frac{3719 601 + 123139}{512} + \frac{19250163008 601 + 490066553408}{2147483648} - 219 - 15601

X Intercepts : (- 1, 0), (2, 0), (3, 0), Y Intercepts : (0, 96)

Asymptotes : None

Extreme Points : Minimum (- 1, 0), Maximum (\frac{21 - 601}{16}, \frac{2269 - 89 601}{8} + \frac{3719 601 - 123139}{512} + \frac{490066553408 - 19250163008 601}{2147483648} - 219 + 15601), Saddle (2, 0), Minimum (\frac{21 + 601}{16}, \frac{2269 + 89 601}{8} - \frac{3719 601 + 123139}{512} + \frac{19250163008 601 + 490066553408}{2147483648} - 219 - 15601)

+1

Interval Notation

Domain : (- \infty, \infty)

Range : [\frac{2269 + 89 601}{8} - \frac{3719 601 + 123139}{512} + \frac{19250163008 601 + 490066553408}{2147483648} - 219 - 15601, \infty)

Solution steps

Domain of

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

Range of

(x + 1)^{2} (x - 2)^{5} (x - 3) : f (x) \geq \frac{2269 + 89 601}{8} - \frac{3719 601 + 123139}{512} + \frac{19250163008 601 + 490066553408}{2147483648} - 219 - 15601

Axis interception points of

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

X Intercepts

: (- 1, 0), (2, 0), (3, 0),

Y Intercepts

: (0, 96)

Asymptotes of

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

None

Extreme Points of

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

Minimum

(- 1, 0),

Maximum

(\frac{21 - 601}{16}, \frac{2269 - 89 601}{8} + \frac{3719 601 - 123139}{512} + \frac{490066553408 - 19250163008 601}{2147483648} - 219 + 15601),

Saddle

(2, 0),

Minimum

(\frac{21 + 601}{16}, \frac{2269 + 89 601}{8} - \frac{3719 601 + 123139}{512} + \frac{19250163008 601 + 490066553408}{2147483648} - 219 - 15601)

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Frequently Asked Questions (FAQ)

What is the f(x)=(x+1)^2(x-2)^5(x-3) ?
The f(x)=(x+1)^2(x-2)^5(x-3) is