Free Printable ch5 and ch6

1.

The function f (x) = |x| + |x – 1| is

a)

continuous at x = 0 as well as at x = 1.

b)

continuous at x = 1 but not at x = 0.

c)

discontinuous at x = 0 as well as at x = 1.

d)

continuous at x = 0 but not at x = 1.

2.

$Iff(x)=2x\ and\ g(x)=\frac{x^2}{2}+1,\ then\ which\ of\ the\ following\ can\ be\ a\ discontinuous\ function$

a)

$f(x)+g(x)$

b)

$f(x)-g(x)$

c)

$f(x).g(x)$

d)

$\frac{f(x)}{g(x)}$

3.

$Find\ the\ derivative\ of\cot^2x^3$

a)

$2\cot x^3$

b)

$-2\cot x^3\operatorname{cosec}^2x^3$

c)

$-6x^2\operatorname{cosec}^2x^3.\cot x^3$

d)

$-6x^2\operatorname{cosec}^2x^3.$

4.

$Is\ the\ function\ defined\ by\ f(x)=x^2–\sin x+5\ continuous\ at\ x=\pi?$

a)

yes

b)

no

5.

Find the derivative of

a)

$\frac{1}{1+x^2}$

b)

$\frac{2}{1+x^2}$

c)

$\frac{3}{1+x^2}$

d)

$\frac{4}{1+x^2}$

6.

$Find\ \ \frac{dy}{dx}\ of\ x=a\ (\cos\theta+\theta\sin\theta),y=a(\sin\theta\ –\ \theta\cos\theta)$

a)

$\sin\theta$

b)

$\cos\theta$

c)

$\tan\theta$

d)

$\cot\theta$

7.

$Find\ the\ \sec ond\ order\ derivative\ of\ x^{20}$

a)

$120x^{19}$

b)

$120x^{18}$

c)

$380\ x^{18}$

d)

$380\ x^{19}$

8.

$Differentiate\ \sin^2x\ w.r.t\ e^{\cos\ x}$

a)

$\frac{\cos x}{e^{\cos\ x}}$

b)

$-\frac{2\cos x}{e^{\cos x}}$

c)

$\frac{2\cos2x}{e^{\cos x}}$

d)

$-\frac{2\cos2x}{e^{\cos x}}$

9.

$Differentiate\ \sqrt{e^{\sqrt{x}}}\ ,\ x>0\ with\ respect\ to\ x.$

a)

$\frac{e^{\sqrt{x}}}{\sqrt{xe^{\sqrt{x}}}}$

b)

$\frac{e^{\sqrt{x}}}{4\sqrt{xe^{\sqrt{x}}}}$

c)

$\frac{e^{\sqrt{x}}}{-4\sqrt{xe^{\sqrt{x}}}}$

d)

$\frac{4e^{\sqrt{x}}}{\sqrt{xe^{\sqrt{x}}}}$

10.

$Differentiate\ \log_7\left(\log\ x\right)\ with\ respect\ to\ x$

a)

$\frac{1}{\log7\log x}$

b)

$\frac{\log x}{\log7\log x}$

c)

$\frac{1}{x\log7\log x}$

d)

$\frac{x}{\log7\log x}$

11.

$Differentiate\ \cot^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right]\ ,\ 0<x<\frac{\pi}{2}$

a)

$\frac{2}{3}$

b)

$\frac{1}{2}$

c)

$\frac{3}{2}$

d)

$\frac{3}{4}$

12.

$Find\ \frac{dy}{dx}\ of\ \ xy=e^{\left(x-y\right)}$

a)

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

b)

$\frac{1}{x\left(y+1\right)}$

c)

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

d)

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

13.

$Find\ \frac{dy}{dx}\ of\ \ xy=e^{\left(x-y\right)}$

a)

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

b)

$\frac{1}{x\left(y+1\right)}$

c)

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

d)

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

14.

$Differentiate\ e^{x^3}$

a)

$3x^2e^{x^3}$

b)

$6x^2e^{x^3}$

c)

$3x^{ }e^{x^3}$

d)

$6x\ e^{x^3}$

15.

Derivative of sinx w.r.t. cosx

(a)

16.

Local maximum point is obtained when

a)

$f'\left(x\right)$ exchange from negative to positive

b)

$f''\left(x\right)$ exchange from positive to negative

c)

$f'\left(x\right)$ exchange from positive to negative

d)

$f''\left(x\right)$ exchange from negative to positive

17.

Over what interval(s) $f\left(x\right)$ is increasing?

a)

$\left(-\infty,-3\right)\cup\left(1,\infty\right)$

b)

$\left(-3,1\right)$

c)

$\left(-5,0\right)\cup\left(2,\infty\right)$

d)

$\left(-5,\infty\right)$

18.

The slope of a function is described by its ____________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

19.

If (a,b) is a local minimum, then what will be true about $f'\left(a\right)$ ?

a)

It's positive

b)

It's negative

c)

It's zero

d)

Cannot be determined

20.

What is the stationary points for the curve

y=x^3+3x^2-24x

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)

21.

Evaluate $\lim_{x\rightarrow0}\frac{\tan\left(x\right)-x}{x^3}$

a)

$\frac{1}{2}$

b)

$-4.5$

c)

$\frac{1}{3}$

d)

$\frac{1}{4}$

22.

What is the absolute minimum value for the function $f\left(x\right)=2x^2+4x-1$ ?

a)

$-1$

b)

$-4$

c)

$4$

d)

$-3$

23.

Find

\frac{\text{d}y}{\text{d}x}

given that

y^2+xy=\cos\left(y\right)

a)

$2y+x$

b)

$-\frac{y}{2y+x+\sin\left(y\right)}$

c)

$\frac{\sin\left(y\right)-y}{2y+x}$

d)

$-y-xy$

24.

The slope of a function is described by its ____________.

a)

first derivative

b)

second derivative

c)

third derivative

d)

expression

25.

Find the equation of the tangent to the curve $y\ =\ 4x^2\ -\ 12x\ +\ 7\ at\ point\ \left(2,\ -1\right).$

a)

y + 4x - 9 = 0

b)

y -4x -9 = 0

c)

y - 4x + 9 = 0

d)

y + 4x + 9 = 0

26.

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

27.

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

28.

What is the equation of the tangent line at x = 1 $of$ $f\left(x\right)=\ \sqrt{x}$

a)

$y=\frac{1}{2}x-\frac{1}{2}$

b)

$y=\frac{1}{2}x+\frac{1}{2}$

c)

$y=2x-1$

d)

$y=2x$

29.

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

a)

y+1=2(x+1)

b)

y=2x-1

c)

y=2x+2

d)

y= -x-1

30.

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)

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

31.

Find the equation of the tangent line at the point (-1,1) of: $f\left(x\right)\ =\ x^4$

a)

$y=-\frac{1}{4}x-3$

b)

$y=-4x-3$

c)

$y=\frac{1}{4}x+3$

d)

$y=4x+3$

32.

Find the slope of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

33.

Find the slope of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

34.

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

35.

Find the slope of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

36.

Find the slope of f(x) = -3x² – 6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

37.

Write the slope of the line tangent to the graph of y=x² – 2 at the point x = -8.

a)

2

b)

-4

c)

-8

d)

-16

38.

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

a)

$-\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{3}{4}$

d)

$-\frac{4}{3}$

ch5 and ch6

Total questions: 38

Worksheet time: 1hrs 16mins

Similar Resources on Wayground