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Popular >

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

Solution

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

Solution

Domain : - \infty < x < \infty

Range : f (x) \leq \frac{21}{4}

X Intercepts : \frac{1 + 21}{2}, 0, - \frac{1 + 21}{2}, 0, Y Intercepts : (0, 5)

Asymptotes : None

Extreme Points : Maximum (- \frac{1}{2}, \frac{21}{4}), Minimum (0, 5), Maximum (\frac{1}{2}, \frac{21}{4})

+1

Interval Notation

Domain : (- \infty, \infty)

Range : (- \infty, \frac{21}{4}]

Solution steps

Domain of

- x^{4} + x^{2} + 5 : - \infty < x < \infty

Range of

- x^{4} + x^{2} + 5 : f (x) \leq \frac{21}{4}

Axis interception points of

- x^{4} + x^{2} + 5 :

X Intercepts

: \frac{1 + 21}{2}, 0, - \frac{1 + 21}{2}, 0,

Y Intercepts

: (0, 5)

Asymptotes of

- x^{4} + x^{2} + 5 :

None

Extreme Points of

- x^{4} + x^{2} + 5 :

Maximum

(- \frac{1}{2}, \frac{21}{4}),

Minimum

(0, 5),

Maximum

(\frac{1}{2}, \frac{21}{4})

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f (x) = \frac{x ^{4}}{4} + \frac{x ^{3}}{2} - \frac{x ^{2}}{2} + 8

y = - \frac{1}{4} x - 7

Frequently Asked Questions (FAQ)

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