Free Printable Extremum problem

1.

Find the coordinates of the stationary points of the function

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

a)

(-3,35)

b)

(3,1)

c)

(3,-1)

d)

(-3,-1)

2.

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

3.

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)

4.

Find the values of x such that $f'\left(x\right)=0$ for

f\left(x\right)=x^4-18x^2

. (The answer can be more than 1)

a)

-3

b)

0

c)

1

d)

3

5.

Find the coordinates of the stationary points for

y=-x^3+3x^2

a)

(2,4) & (0,0)

b)

(1,2) & (0,0)

c)

(3,6) & (0,0)

d)

(4,8) & (0,0)

6.

Determine the maximum or minimum, if any, for

y=-x^3+3x^2

a)

max point: (3,6) & min point: (0,0)

b)

max point: (2,4) & min point: (0,0)

c)

max point: (3,6) & min point: (0,0)

d)

max point: (4,8) & min point: (0,0)

7.

Find the relative maximum or minimum point on the curve

y=2x^3+3x^2-12x-4

by using second derivative test.

a)

(1,11) max point, (-2,-16) min point

b)

(1,-11) min point, (-2,16) max point

c)

(1,-16) max point, (-2,11) min point

d)

(-1,11) max point, (2,-16) min point

8.

Function f is given by

f\left(x\right)=x^3-3x^2-9x

. By using second derivative test (SDT), find the local extremum. (The answer can be more than 1)

a)

(-1, 5) is local maximum

b)

(-1,5) is local minimum

c)

(3, -27) is local minimum

d)

(3, -27) is local maximum

9.

If $\frac{\text{d}^2x}{\text{d}y^2}>0$ , turning point is a

a)

maximum point

b)

minimum point

c)

point of inflexion

10.

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

a)

TRUE

b)

FALSE

Extremum problem

Total questions: 10

Worksheet time: 5mins

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