Free Printable Q2 Quiz 1 in Basic Calculus

1.

Which of the following statements CORRECTLY describes the derivative of a function?

a)

It is used to describe the rate of change of a function f(x).

b)

The derivative is the slope of the secant lines intersecting the curves.

c)

The derivative of a function defines how narrow or how wide a parabola will be.

d)

The derivative of a function is never negative.

2.

Find the slope of the line tangent to the curve y = x^2 - 2x + 1 at x = -1.

(a)

3.

Find the slope of the line tangent to the curve of f(x) = x^3 - 2x^2 + 5x at x = 1.

(a)

4.

Find the equation of the line tangent to the curve of h(x) = 1/x-1 at x = 2.

a)

y = -x-3

b)

y = -x+3

c)

y = x - 3

d)

y = x+3

5.

Find the equation of the line tangent to the curve f(x) = sin x at x = 0.

(a)

6.

Determine the derivative of the function f(x) = (x-2)/(x^2 - 4) at x = 2.

a)

2

b)

1

c)

-2

d)

Not differentiable at x = 2

7.

Find the equation of the line tangent to the curve g(x) = cos x at x = 0.

a)

y = 0

b)

y = -1

c)

y = 1

d)

The tangent line does not exist.

8.

Find the general derivative of the function f(x) = x^2 - 2x + 1.

a)

f'(x) = -2x + 2

b)

f'(x) = 2x - 2

c)

f'(x) = -2x - 2

d)

f'(x) = 2x + 2

9.

On which of the following points is the function f(x) = $\frac{x-2}{x^2-4}$ ?

a)

2

b)

-2

c)

$\sqrt[]{2}$

d)

4

10.

Find the general derivative of the function f(x) = $\sqrt[]{x-5}$ ?

a)

f'(x) = $\frac{1}{2\sqrt[]{x-5}}$

b)

f'(x) = $-\frac{1}{2\sqrt[]{x-5}}$

c)

f'(x) = $\frac{1}{2\sqrt[]{x+5}}$

d)

The derivative does not exist.

11.

Find the derivative of the function f(x) = e^x.

a)

f(x) = -e^x

b)

f(x) = e^-x

c)

f(x) = e^x

d)

f(x) = 1/e^2x

12.

Find the equation of the line tangent to the function f(x) = 4x^2 - 2x + 5 at x = 0.

a)

y = -2x + 5

b)

y = -2x - 5

c)

y = 2x + 5

d)

y = 2x - 5

13.

Find the equation of the line tangent to the function h(x) = $\sqrt[]{2x-3}$ .

a)

$y=-\frac{\sqrt[]{7}}{7}x-\frac{2\sqrt[]{7}}{7}$

b)

$y=-\frac{\sqrt[]{7}}{7}x+\frac{2\sqrt[]{7}}{7}$

c)

$y=\frac{\sqrt[]{7}}{7}x-\frac{2\sqrt[]{7}}{7}$

d)

$y=\frac{\sqrt[]{7}}{7}x+\frac{2\sqrt[]{7}}{7}$

14.

Find the slope of the line tangent to the curve f(x) = $\sqrt[]{\frac{x}{7}}$ at x = 2.

a)

$\frac{\sqrt[]{14}}{28}$

b)

$-\frac{\sqrt[]{14}}{28}$

c)

$\sqrt[]{14}$

d)

$-\sqrt[]{14}$

15.

Which of the following statement(s) is/are CORRECT?

a)

A function continuous at x = a is differentiable at x = a.

b)

A function differentiable at x = a is continuous at x = a.

c)

A function not continuous at x = a is not differentiable at x = a.

d)

A function not differentiable at x = a is not continuous at x = a.

Q2 Quiz 1 in Basic Calculus

Total questions: 15

Worksheet time: 26mins

Similar Resources on Wayground