What is the f(x)=4x^6-4x^5+x^4-4x^2+4x-1 ?

The f(x)=4x^6-4x^5+x^4-4x^2+4x-1 is

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f(x)=4x^6-4x^5+x^4-4x^2+4x-1

f (x) = 4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1

Domain : - \infty < x < \infty

Range : f (x) \geq - 4.38050 \dots

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

Asymptotes : None

Extreme Points : Minimum (- 0.68840 \dots, - 4.38050 \dots), Maximum (\frac{1}{2}, 0), Minimum (0.85908 \dots, - 0.23483 \dots)

Interval Notation

Domain : (- \infty, \infty)

Range : [- 4.38050 \dots, \infty)

Solution steps

Domain of

4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1 : - \infty < x < \infty

Range of

4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1 : f (x) \geq - 4.38050 \dots

Axis interception points of

4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1 :

X Intercepts

: (\frac{1}{2}, 0), (- 1, 0), (1, 0),

Y Intercepts

: (0, - 1)

Asymptotes of

4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1 :

None

Extreme Points of

4 x^{6} - 4 x^{5} + x^{4} - 4 x^{2} + 4 x - 1 :

Minimum

(- 0.68840 \dots, - 4.38050 \dots),

Maximum

(\frac{1}{2}, 0),

Minimum

(0.85908 \dots, - 0.23483 \dots)

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

f (x) = cos (x) cos (300 x) + ∣ x ∣ - 0.7

y = \frac{3}{5 x}

f (a) = 2 a^{3} - 4 a^{2} + 5 a - 12

f (x) = - (x - 2)^{2} - 1