MATH160 Jeopardy!!!!!!!

Derivatives

100

Find the derivative: f(x) = 4x⁵ -3x² +7 

20x⁴ - 6x

200

Find the derivative: f(x) = 6x³ - 8x + 2

18x² - 8

300

Find the derivative: f(x) = 5x³ - 2x² + 8x - 1

15x² - 4x + 8

400

Find the derivative: f(x) = 7x⁴ - 3x³ + 5x² - 9

28x³ - 9x² + 10x

500

Find the derivative: f(x) = 3x⁵ - 4x⁴ + 7x² - 6x + 10

15x⁴ - 16x³ + 14x - 6

MORE CRITICAL NUMBERS!!!

100

Find the critical numbers:

f(x) = x² + 6x

x = -3

200

Find the critical numbers:

f(x) = x² - 10x + 3

x = 5

300

Find the critical numbers:

f(x) = x³ - 12x

x = -2, 2

400

Find the critical numbers:

f(x) = 3x² + 12x

x = -2

500

Find the critical numbers:

f(x) = 2x² - 8x

x = 2

Higher-Order Derivatives

100

What is f′′(x) called?

The second derivative

200

Find f′′(x):

f(x)=3x⁴−5x²+7x

f′′(x)=36x²−10

300

 Find f′′(x):

f(x)=5x³−2x³+8x−1

f''(x)= 30x - 4

400

Find f′′′(x):

f(x)=2x⁵ − 4x³ + x

f′′′(x)=120x² − 24

500

f(x)=x⁶−3x⁴+2x² , Find f'''(x)

f′′′(x)=120x³−72x

Critical Numbers 1

100

Find the critical numbers:

f(x) = x² - 6x + 5

x = 3

200

Find the critical numbers:

f(x) = x² + 8x + 12

x = -4

300

A student finds f′(x)=2x−8 and says the critical number is x=8. Are they correct and if not what is the correct answer?

No, the student is incorrect. x=4

400

A student finds f′(x)=3x² and says there are two critical numbers, x=0 and x = -0. What is wrong?

0 and −0 are the same number, so there is only one critical number.

500

What is the first step in finding critical numbers?

Find the derivative

Critical Numbers 2

100

What equation do you usually solve to find critical numbers?

f'(x) = 0

200

Find the critical number(s). 

f(x)=x²+2x

x = -1

300

Find the critical number(s). 

f(x) = x³−3x

x = -1, 1

400

Find the critical numbers:

f(x) = x² - 4x

x = 2

500

Find the critical numbers:

f(x) = x²

x= 0