Free Printable You Derive Me Crazy

1.

Find the derivative of and simplify:

a)

12x⁴ +3x²

b)

20x⁴+3x² +16

c)

3x⁵ +32x³ +6x² +8x

d)

24x³

2.

Find the derivative of and simplify:

a)

$8x^4-60x^2$

b)

$\frac{10x^4-60x^2}{2x^2-5}$

c)

$\frac{8x^4-60x^2}{\left(2x^2-5\right)^2}$

d)

$\frac{12x^2}{4x}$

3.

Which if the following is NOT the correct notation for the first derivative of a function?

a)

$f'\left(x\right)$

b)

$y'$

c)

$dy$

d)

$\frac{dy}{dx}$

4.

How do you find horizontal tangent lines?

a)

Find where the derivative is undefined

b)

Find where the derivative equals zero

c)

Find where the derivative is 1

d)

Find where the derivative is negative

5.

The first derivative tells you the...

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

slope of the secant line

6.

The derivative of (leave in raw form)

a)

y'=2x-x^-2

b)

y'=x^-1+8x

c)

y'=x^-2+8x

d)

y=8x-x^-2

7.

The derivative of a function is its

a)

Slope of secant

b)

Maximum/Minimum

c)

Instantaneous rate of change

d)

Common Denominator

8.

The position of a function at time, t seconds is given by:
s(t) = -4.9t² + 20t + 200
What is the initial position of the function?

a)

20 meters

b)

200 meters

c)

-4.9 meters

d)

Not enough information

9.

If the position of a free-falling object is given by the function:
s(t) = -4.9t² + 20t + 200
What is it's velocity at 3 seconds?

a)

215.9 m/s

b)

9.4 m/s

c)

-9.4 m/s

d)

Cannot be determined

10.

Find the derivative of:
f(x) = 3(x⁴ - 5x)⁵
(Leave your answer in raw form)

a)

f(x) = 15(x⁴ - 5x)⁴(4x³ - 5)

b)

f(x) = 15(4x³ - 5)⁴

c)

f(x) = 15(x⁴ - 5x)⁴

d)

f(x) = 15(4x³ - 5)⁴(12x²)

11.

Find the second derivative of:

y = (3x² - 4x)³

(Raw Form for Final answer)

a)

$y''=18\left[2\left(6x-4\right)\right]$

b)

$y''=\left(18x-12\right)\left[2\left(3x^2-4x\right)\right]+18\left(3x^2-4x\right)^2$

c)

$y''=\left(18x-12\right)\left[2\left(3x^2-4x\right)\left(6x-4\right)\right]+18\left(3x^2-4x\right)^2$

d)

$y''=18x\left[2\left(6x-4\right)\right]+18\left(3x^2-4x\right)^2$

12.

This tells you the average velocity of an object over the time interval [a, b].

a)

$\frac{v'\left(a\right)+v'\left(b\right)}{a-b}$

b)

$\frac{s\left(b\right)-s\left(a\right)}{b-a}$

c)

$\frac{v\left(b\right)-v\left(a\right)}{b-a}$

d)

$\frac{v\left(a\right)+v\left(b\right)}{2}$

13.

When writing an equation of the tangent line at a point for the function f(x), how do you find its slope?

a)

$f\left(x_1\right)$

b)

$\frac{f\left(b\right)-f\left(a\right)}{b-a}$

c)

$f'\left(x_1\right)$

14.

Find

$\frac{d^3y}{dx^3}$ when: $\frac{dy}{dx}=4x^3-2x^{-1}$

Simplify your answer.

a)

$24-12x^2$

b)

$24x-4x^2$

c)

$\frac{24x^3+12}{x^4}$

d)

$\frac{24x^4-4}{x^3}$

15.

Find the first derivative of: $f\left(x\right)=2x\left(4-3x^2\right)^4$

Answers are in raw form

a)

$f'\left(x\right)=2x\left[4\left(4-3x^2\right)^3\right]+2\left(4-3x^2\right)^4$

b)

$f'\left(x\right)=2x\left[4\left(4-3x^2\right)^3\left(-6x\right)\right]+2\left(4-3x^2\right)^4$

c)

$f'\left(x\right)=8x\left(4-3x^2\right)^3\left(-6x\right)$

d)

$f'\left(x\right)=2\left[4\left(4-3x^2\right)^3\left(-6x\right)\right]$

16.

What topics do you need to practice?

4 lines

You Derive Me Crazy

Total questions: 16

Worksheet time: 25mins

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