Analyzing function behavior

9000079107

Level:

What is the function value of the function

f

at its local minimum?

f (x) = \frac{2}{\sqrt{4 x - x^{2}}}

1

2

0

the local minimum does not exist

9000079101

Level:

Find the intervals of monotonicity for the following function.

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

Decreasing on

(- \infty; \frac{5}{2})

and

(\frac{5}{2}; \infty)

Decreasing on

(- \infty; \frac{5}{2}) \cup (\frac{5}{2}; \infty)

Decreasing on

(- \infty; \frac{5}{2})

, increasing on

(\frac{5}{2}; \infty)

Increasing on

(- \infty; \frac{5}{2})

, decreasing on

(\frac{5}{2}; \infty)

9000079102

Level:

Find the intervals where the following function is a decreasing function.

f (x) = \frac{x^{2} + 1}{x}

[- 1; 0)

and

(0; 1]

[- 1; 1]

(- \infty; - 1]

and

[1; \infty)

[1; \infty)

9000079103

Level:

Find the

x

at which has the function

f

a local maximum.

f (x) = x^{3} - 3 x^{2} - 9 x + 2

x = - 1

x = - 3

x = 1

x = 3

9000079104

Level:

Find the

x

at which has the function

f

a local minimum.

f (x) = \frac{\ln x}{x}

does not exist

x = 0

x = 1

x = e

9000079105

Level:

Find all the

x

at which the function

f

has local extrema.

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

x = 0

x_{1} = 0

x_{2} = 1

x_{1} = - 1

x_{2} = 1

x_{1} = - 1

x_{2} = 0

x_{3} = 1

9000079106

Level:

Given function

f (x) = x e^{\frac{1}{x}}

, identify a true statement.

The local minimum of the function

f

is at the point

x = 1

, the function does not have a local maximum.

The local maximum of the function

f

is at the point

x = 0

, the local minimum at

x = 1

The local maximum of the function

f

is at the point

x = 1

, the function does not have a local minimum.

The function

f

has neither local minimum nor maximum.

9000070407

Level:

Given the function

f (x) = - x^{3} + 3 x^{2} + 9 x - 1

, find the intervals where

f

is a decreasing function.

(3; \infty)

(- \infty; 1)

(- 1; 3)

(1; \infty)

9000070408

Level:

Given the function

f (x) = - x^{3} + 3 x^{2} + 45 x - 12

, find the intervals where

f

is an increasing function.

(- 3; 5)

(- \infty; - 3)

(5; \infty)

(- 12; 45)

9000070409

Level:

Given the function

f (x) = \frac{x^{2}}{x - 2}

, find the intervals where

f

is a decreasing function.

(0; 2)

(- \infty; - 1)

(5; \infty)

(2; 5)

Analyzing function behavior

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