Free Printable Application of Derivatives 12th

1.

What is the increasing interval for the function below?

a)

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

b)

$\left(-\infty,2\right]$

c)

$\left(-\infty,6\right]$

d)

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

2.

What is the decreasing interval(s) on the function shown?

a)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

b)

$\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

c)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

d)

$\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

3.

The intervals in which the function f given by f (x) = x² – 4x + 6 is increasing is

a)

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

b)

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

c)

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

d)

none of these

4.

The logarithmic function is increasing on

a)

$\left(0,\ 1\right)$

b)

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

c)

$\left(1,\ \infty\right)$

d)

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

5.

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)

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

6.

The interval on which the function f (x) = 2x³ + 9x² + 12x – 1 is decreasing is:

a)

$\left[-1,\ \infty\right)$

b)

$\left[-2,\ -1\right]$

c)

$\left(-\infty,\ -2\right]$

d)

$\left[-1,\ 1\right]$

7.

Which of the following functions is decreasing on $\left(0,\ \frac{\pi}{2}\right)$

a)

$\sin2x$

b)

$\tan x$

c)

$\cos x$

d)

$\cos3x$

8.

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)

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

9.

y = x (x – 3)² decreases for the values of x given by :

a)

$1<x<3$

b)

$x<0$

c)

$x>0$

d)

$0<x<\frac{3}{2}$

10.

If $\frac{\text{d}x}{\text{d}y}=\infty$ , then the tangent at a point P(x,y) on the curve is perpendicular to the x- axis.

a)

False

b)

True

11.

For Maximum point : (i) $\frac{\text{d}x}{\text{d}y}=0$ ; (ii) $\frac{d^2y}{dx^2}$ < 0

a)

False

b)

True

12.

The smallest value of the polynomial

x^3-18x^2+96x

in [0, 9] is

a)

126

b)

0

c)

135

d)

160

13.

The maximum value of

\sin x.\cos x

is

a)

1/4

b)

1/2

c)

$\sqrt{2}$

d)

$2\sqrt{2}$

14.

The absolute maximum and the absolute minimum values of the function $f\left(x\right)=4x-\frac{x^2}{2}$ in [-2, 4.5] is

a)

8, -10

b)

4, - 2

c)

0, 3

d)

3, 6

15.

The points at which the function changes its nature from increasing to decreasing or from decreasing to increasing are called

(a)

16.

The slope of the normal to the curve $x=a\cos^3\theta,\ \ y=a\sin^3\theta$ at $\theta=\frac{\pi}{4}$ is

(a)

17.

The equation of the tangent line to the curve y = x² – 2x +7 which is parallel to the line 2x – y + 9 = 0 is

a)

$y\ –\ 2x\ –\ 3=0$

b)

$y\ +2x\ –\ 3=0$

c)

$y\ –\ 2x\ +\ 3=0$

d)

$y\ +2x\ +\ 3=0$

18.

The equation of normal to the curve y = tan x at (0, 0) is ________

a)

$x-y=0$

b)

$x+y=1$

c)

$x+y=0$

d)

$x-y=1$

19.

The equation of the normal to the curve $y=x^4–\ 6x^3+13x^2\ –\ 10x+5$ at $\left(0,\ 5\right)$ is

a)

$x\ \ +10y+50=0$

b)

$x\ –\ 10y+50=0$

c)

$x\ –\ 10y-50=0$

d)

$x\ +10y+50=0$

20.

The equations of all lines having slope 0 which are tangent to the curve $y=\frac{1}{x^2-2x+3}$ is

a)

$y=1$

b)

$2y=1$

c)

$2y+1=0$

d)

$y+1=0$

21.

Determine the point on the curve f(x)=(2x-1)² where the tangent is parallel to the line y=4x-2

a)

(0 , 1)

b)

(1 , 9)

c)

(1/2 , 0)

d)

(1 , 1)

22.

What is the equation of the normal line to the curve $y=3x^2+2x$ at $x=1$ ?

a)

$y=8x-3$

b)

$y=8x-13$

c)

$y=-\frac{1}{8}x+\frac{41}{8}$

d)

$y=\frac{1}{8}x+\frac{39}{8}$

23.

The point on the curve y²=xat which the tangent is parallel to the line joining (1,4) and (3,2) is

a)

(5,6)

b)

(1/2,-1/2)

c)

(1/2,3/2)

d)

(-1/2,1/2)

24.

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

25.

Find the equation of the normal line at x = 0 of:
$f\left(x\right)\ =\ x^3+e^x$

a)

$y=-x+1$

b)

$y=\ x+1$

c)

$y=-x\ -1$

d)

$y=x\ -\ 1$

Application of Derivatives 12th

Total questions: 25

Worksheet time: 1hrs 15mins

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