Free Printable Functions and Their Derivatives

1.

What is the slope of the curve y = 2sin(x) at x = π/3

a)

-√3

b)

√3

c)

-1

d)

1

2.

Which one is the product rule?

a)

f(x)g(x)

b)

f'(x)g(x)-f(x)g'(x)

c)

f'(x)g(x)+f(x)g'(x)

d)

f'(x)g'(x)+f'(x)g'(x)

3.

Find an equation of the line tangent to the curve f(x)=(x-2)(x+1) at the point (1,3)

a)

y=x-2

b)

y=x+2

c)

y=6x+1

d)

y=x

4.

At what point on the graph of $y=\frac{1}{2}x^2$ is the tangent line parallel to the line $y=\frac{1}{2}x-5$ ?

a)

(0.5, 0.5)

b)

(0.5, 0.125)

c)

(1, 0.25)

d)

(1, 0.5)

e)

(2, 2)

5.

The slope of $f\left(x\right)=x^3+12x-6$ at x = 4 is:

a)

48

b)

-60

c)

60

d)

96

e)

DNE

6.

Let $f\left(x\right)=\frac{3x-2}{2x+1}$ . Find f'(x).

a)

$\frac{3}{2}$

b)

$-\frac{7}{\left(2x+1\right)^2}$

c)

$\frac{12x+1}{\left(2x+1\right)^2}$

d)

$\frac{12x-1}{\left(2x+1\right)^2}$

e)

$\frac{7}{\left(2x+1\right)^2}$

7.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If Find

a)

$\frac{3}{2}$

b)

$\frac{-3}{2}$

c)

$\frac{-1}{2}$

d)

1

8.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$ Find $h'\left(2\right)$

a)

$\frac{3}{2}$

b)

$2$

c)

$\frac{5}{6}$

d)

$-3$

9.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If Find

a)

$0$

b)

$2$

c)

$\frac{5}{2}$

d)

$-3$

10.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If Find

a)

$-1$

b)

$2$

c)

$\frac{5}{2}$

d)

$-3$

Functions and Their Derivatives

Total questions: 10

Worksheet time: 10mins

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