Free Printable Extremum Problems

1.

If a function has a second derivative that is negative, what does that tell you?

a)

The function is increasing.

b)

The function is decreasing.

c)

The function has a local minimum.

d)

The function has a local maximum.

2.

If a function has a second derivative that is positive, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The function has a local minimum

d)

The function has a local maximum

3.

The slope of a function is described by its ____________.

a)

First derivative

b)

Second derivative

c)

Third derivative

d)

Expression

4.

If $\frac{dy}{dx}$ is a positive, then the function is...

a)

a maximum

b)

a minimum

c)

decreasing

d)

increasing

5.

If $\frac{dy}{dx}$ is a negative, then the function is...

a)

a maximum

b)

a minimum

c)

decreasing

d)

increasing

6.

The function contains...

a)

One local maximum.

b)

Two local maximum.

c)

Two local minimum.

d)

Three local maximum.

7.

Given that

f\left(x\right)=x^2-6x+8^{ }

. Find the stationary point and determine it's nature.

a)

(-1, 3) is max point

b)

(-1,3) is min point

c)

(3, -1) is min point

d)

(3, -1) is max point

8.

Find the critical points of a given function,

f\left(x\right)=x^3-3x+2

.

a)

(1,0)

b)

(-1,0) and (1,-4)

c)

(-1,-4) and (1,0)

d)

(-1,4) and (1,0)

9.

$\frac{\text{d}^2x}{\text{d}y^2}=-12$ , the nature of this function is minimum.

a)

TRUE

b)

FALSE

10.

Find the relative extremum of the curve $y=x^3+2x^2-4x+4$ .

a)

$\left(\frac{2}{3},\frac{68}{27}\right)$ is a relative maximum point.

b)

$\left(\frac{2}{3},\frac{68}{27}\right)$ is a relative minimum point.

c)

$\left(-2,12\right)\$ is a relative maximum point.

d)

$\left(-2,12\right)\$ is a relative minimum point.

Extremum Problems

Total questions: 10

Worksheet time: 50mins

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