Applications of derivatives | math4u.vsb.cz

9000079108

Level:

C

Find the

x

at which the function

f

has the global minimum on the interval

(- 3; 2]

.

f (x) = x^{3} - 3 x + 4

does not exist

x = - 3

x = - 2

x = 1

9000079109

Level:

C

Find the

x

at which the function

f

has the global maximum on the interval

[1; e]

.

f (x) = x - 2 \ln x

x = 1

x = 2

x = e

x = e - 2

9000145401

Level:

C

Identify a true statement on the function

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

.

The function

f

has a local maximum at the point

x = - 2

.

The function

f

has a local minimum at the point

x = - 2

..

The global maximum of

f

on

R

is at

x = - 2

.

The global minimum of

f

on

R

is at

x = - 2

.

9000145402

Level:

C

Identify a true statement about the function

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

.

The global maximum of

f

on

R

is at

x = 2

and

x = - 2

.

The global minimum of

f

on

R

is at

x = 2

and

x = - 2

.

The function

f

has a local minimum at the point

x = 2

.

The function

f

has a local minimum at the point

x = - 2

.

9000145403

Level:

C

Identify a true statement on the function

f (x) = \frac{4 - 3 x}{x (1 - x)}

.

The function

f

has a local minimum at the point

x = \frac{2}{3}

.

The function

f

has a local maximum at the point

x = \frac{2}{3}

.

The global maximum of

f

on

R ∖ {0.1}

is at

x = \frac{2}{3}

.

The global minimum of

f

on

R ∖ {0.1}

is at

x = \frac{2}{3}

.

9000145404

Level:

C

Identify a true statement about the function

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

.

There is neither local minimum nor maximum of

f

.

The function

f

has a local maximum at the point

x = 1

.

The function

f

has a local minimum at the point

x = 1

.

The global minimum of

f

on

R

is at

x = 1

.

9000145405

Level:

C

Identify a true statement on the function

f (x) = \frac{1}{4} x^{4} - \frac{2}{3} x^{3} - \frac{3}{2} x^{2} + 2 on (- 2; 4)

.

The function

f

has a local maximum at the point

x = 0

.

The function

f

has a local minimum at the point

x = 0

.

The global maximum of

f

on this interval is at

x = 0

.

The global minimum of

f

on this interval is at

x = 0

.

9000145406

Level:

C

Identify a true statement on the function

f (x) = x^{3} - 12 x + 20 on (- 3; 4)

.

The global minimum of

f

on this interval is at

x = 2

.

The global maximum of

f

on this interval is at

x = 2

.

The function

f

has a local minimum at the point

x = - 2

.

The global minimum of

f

on this interval is at the point

x = - 2

.

9000145407

Level:

C

Identify a true statement on the function

f (x) = x^{4} - 8 x^{3} + 22 x^{2} - 24 x + 12

.

The global minimum of

f

on

R

is at

x = 1

and

x = 3

.

The global maximum of

f

on

R

is at

x = 2

.

The local minima of

f

are at

x = 1

and

x = 2

.

The local maximum of

f

is at

x = 3

.

9000145408

Level:

C

Identify a true statement on the function

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

.

The function

f

has neither local minimum nor maximum at

x = 1

.

The global maximum of

f

on

R

is at

x = - 1

.

The function

f

has a local maximum at

x = - \frac{1}{5}

.

The function

f

has three local extrema. These extrema are at

x = 1

,

x = - 1

and

x = - \frac{1}{5}

.