Free Printable Application of Derivatives

1.

A fn is said to be increasing fn if f'(x) is

a)

$\ge0$

b)

$\le0$

c)

$=0$

d)

$\ne0$

2.

A fn is said to be increasing fn if f'(x) is

a)

$\ge0$

b)

$\le0$

c)

$=0$

d)

$\ne0$

3.

Find the interval(s) where f(x)=6x²-x³ is increasing.

a)

(-4,0)

b)

(0,4)

c)

(-∞, 0)∪(4, ∞)

d)

(-∞, -4 )∪(0, ∞)

4.

How many extrema are in the picture?

a)

2

b)

3

c)

4

d)

5

5.

The equation of normal to the curve $3x^2-y^2=8$ which is parallel to the line $x+3y=8$ is

a)

$3x-y=8$

b)

$3x+y+8=0$

c)

$x+3y\ ±\ 8=0$

d)

$x+3y=0$

6.

$The\ function\ f\left(x\right)=\ x^2-8x+12\ is\ strictly\ decrea\sin g\ in$

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(2,\ 6\right)$

c)

$\left(-\infty,\ 4\right)$

d)

$\left(4,\ \infty\right)$

7.

The interval in which $y=x^2e^{–x}$ is increasing is

a)

$\left(-2,\ 0\right)$

b)

$\left(-\infty,\ \infty\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(0,\ 2\right)$

8.

Over what interval(s) is f(x) decreasing?

a)

(-3, 1)

b)

(-∞, -5) ∪ (0, 2)

c)

(-∞, -3) ∪ (1, ∞)

d)

(-5, 0) ∪ (2, ∞)

9.

$The\ angle\ between\ the\ lines\ y\ =\ \sqrt{3}x\ +100\ and\ \ \sqrt{3}y\ =x\ +200\ is$

a)

$60^0$

b)

$30^0$

c)

$90^0$

d)

$45^0$

10.

What are the two numbers that will give the maximum product?

a)

40 and 40

b)

20 and 60

c)

45 and 35

d)

30 and 50

Application of Derivatives

Total questions: 10

Worksheet time: 15mins

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