Free Printable APPLICATION OF DIFFERENTIATION

1.

The slope of a function is described by its ____________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

2.

What is the stationary point for the curve y=x²- 4?

a)

A minimum at ( 0, -4)

b)

A maximum at (0, -4)

c)

A minimum at (0,4)

d)

A maximum at (0,4)

3.

What is the stationary points for the curve f(x) = x³ +3x² - 24x and determine their nature.

a)

Maximum point : (2, -28) and minimum point : (-4, 80)

b)

Minimum point : (2, 28) and maximum point : (-4, 80)

c)

Minimum point : (2, -28) and maximum point : (4, 80)

d)

Minimum point : (2, -28) and maximum point : (-4, 80)

4.

Find the equation of the normal to the curve $y=x^3-2x^2+3$ at the point x=2

a)

4y+x=14

b)

4y+3x=14

c)

y+x=14

d)

4y+x=41

5.

Which of the following statements is true of

f\left(x\right)=-x^3-6x^2-9x-2

?

a)

f is decreasing on $\left(-\infty,\ -3\right)$ .

b)

f is increasing on $\left(-1,\ \infty\right)$

c)

f is decreasing on $\left(-3,\ -1\right)$

d)

f is decreasing on $\left(-\infty,3\right)$

6.

What is the turning point for the curve y=-3x²-12x+5 ?

a)

A minimum at (-2, 17)

b)

A maximum at (-2, 17)

c)

A minimum at (2, -31)

d)

A maximum at (2, -31)

7.

Calculate the gradient of f(x)=ln(x)+x at x=2/3

a)

0.261

b)

2.5

c)

1.5

d)

-0.405

8.

What is the equation of the line tangent to the curve y = x² at x = 1?

a)

y = 2x + 1

b)

y = 2x - 1

c)

y = -2x + 1

d)

y = x - 1

9.

What is the equation of the line tangent to y= x²+2x-1 at x=1?

a)

y=2x

b)

y=4x-2

c)

y=4x

d)

y=2x-2

10.

Write the equation of the normal line of: $f\left(x\right)=2x^2-\frac{1}{x}$ at x = 1

a)

$y=-\frac{1}{5}x+\frac{4}{5}$

b)

$y=5x-6$

c)

$y-1=5\left(x-1\right)$

d)

$y-1=-\frac{1}{5}\left(x-1\right)$

11.

Find the equation of normal for the curve

y=x+\frac{4}{x}

at point (1,5)

a)

y=x/3+14

b)

3y=x+14

c)

y=x+14/3

d)

y/3=x+14

12.

Find the gradient of tangent for

y=x^3+\frac{1}{3}x^2

at point (3,1)

a)

21

b)

11/3

c)

29

d)

83/3

13.

The gradient of tangent to the curve

y=ax^3+bx

at point (1,1) is 4. find the value of a and b.

a)

a=1/2 , b=-1/3

b)

a=3/2, b=-1/2

c)

a=1/3, b=-1/2

d)

a=2 ,b=-2

14.

The total cost (in RM) to produce x units of keyboard per day is given by cost function $C\left(x\right)=2x^3-30x^2+126x+30$ Find the minimum cost.

a)

RM24

b)

RM128

c)

128

d)

RM192

15.

A metal cube is expanding uniformly as it is heated. At time t seconds, the length of each edge of the cube is x cm, and the volume is V cm³.

Given that the volume increases at a constant rate of 0.048 cm³s⁻¹

^{Find dx/dt when x=8}

a)

0.00025 cm/s

b)

9.216 cm/s

c)

0.384 cm/s

d)

4 cm/s

APPLICATION OF DIFFERENTIATION

Total questions: 15

Worksheet time: 3hrs 30mins

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