Free Printable Tangent, Normal and Increasing and decreasing function

1.

Find the slope of the tangent is y= x² -2x at x= 3

a)

-4

b)

4

c)

0

d)

not defined

2.

The point on the curve y² = x where tangent makes 45⁰ angle with x- axis is

a)

(1/2, 1/4)

b)

(1/4,1/2)

c)

(4,2)

d)

(1,1)

3.

Function f(x)= 2x³ -27x +5 is increasing when

a)

x<-3

b)

-3<x<3

c)

$x\le-3$

d)

$-3\le x\le3$

4.

Find the interval in which the function f(x) = 10-6x-2x² is decreasing is

a)

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

b)

$x>-\frac{3}{2}$

c)

-3/2

d)

3/2

5.

The function f(x)= x - sinx is increasing in

a)

R

b)

(-2,2)

c)

(-5,5)

d)

R⁺

6.

What is the equation of the tangent to the curve f(x)= 4x²+2x-1 at the point x=0?

a)

y+1=2(x+1)

b)

y = 2x - 1

c)

y=2x+2

d)

y = 2x -3

7.

If f '(x) = 0, what does that mean with respect to the tangent line?

a)

Tangent line is vertical

b)

Tangent line has a positive slope

c)

Tangent line is horizontal

d)

Tangent line has a negative slope

8.

The normal to the curve is

a)

the derivative

b)

the integral

c)

perpendicular to the tangent to the curve

d)

the tangent to the curve

9.

If the SLOPE of the tangent is $\frac{4}{3}$ , what is the slope of the normal at the same point?

a)

$-\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$-\frac{4}{3}$

10.

What is the slope of the line normal to the curve y = x² + x at x = 1?

a)

-1

b)

-1/2

c)

-1/3

d)

-1/4

11.

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

12.

Intervals in which the function given by $f\left(x\right)=\sin3x$ , $x\in\left[0,\ \frac{\pi}{2}\right]$ is decreasing

a)

$\left(\frac{\pi}{6},\ \frac{\pi}{2}\right]$

b)

$\left[0,\ \frac{\pi}{6}\right)$

c)

$\left[0,\ \frac{\pi}{3}\right)$

d)

$\left(\frac{\pi}{3},\ \frac{\pi}{2}\right]$

13.

The logarithmic function is increasing on

a)

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

b)

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

c)

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

d)

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

14.

In the interval (- 1, 1), function f given by $f(x)=x^2–\ x+1$ is

a)

increasing

b)

decreasing

c)

increasing and decreasing both

d)

neither increasing nor decreasing

15.

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)

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

16.

The function f (x) = tan x – 4x is strictly decreasing on

a)

$\left(-\frac{\pi}{3},\ \frac{\pi}{3}\right)$

b)

$\left(\frac{\pi}{3},\ \frac{\pi}{2}\right)$

c)

$\left(-\frac{\pi}{2},\ -\frac{\pi}{3}\right)$

d)

none of these

17.

Intervals in which the function $y=x^4-\frac{4x^3}{3}$ is strictly increasing is

a)

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

b)

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

c)

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

d)

none of these

18.

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)

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

19.

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

a)

$1<x<3$

b)

$x<0$

c)

$x>0$

d)

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

20.

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

a)

$\sin2x$

b)

$\tan x$

c)

$\cos x$

d)

$\cos3x$

Tangent, Normal and Increasing and decreasing function

Total questions: 20

Worksheet time: 20mins

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