Calculus Jeopardy

Derivatives

100

y=4x³ + 7x²+ 2x + 3

y¹=12x² + 14x + 2

200

y=√1+2x+2x

y¹= 4

300

y=x²+3x+5

y¹=2x+3

400

y= -1/4x+1

y¹=-1/4

500

y=cos(2x+3)

y¹=-2sin(2x+3)

Definitions

100

What is the definition of Calculus? 

The study of rates of change

200

What is the definition of a secant line? 

The average rate of change (slope) 

300

What is the definition of a tangent line? 

The instantaneous rate of change (derivative)

400

What is the definition of a difference quotient? 

The measure of the average rate of change of the function over an interval

500

What are the four concepts of Calculus? 

1. Limits 

2. Differentiation 

3. Integration

4 Function Theory 

Notations, & Differentiation

100

What is Leibniz's notation? 

dy/dx

200

What is Lagrange's notation?

f¹(x)

300

Y = 12x⁵ + 3x⁴+ 7x³ + x² − 9x + 6 Find d⁴y/dx⁴

f^IIII(x)=1440x + 72

400

y=4x⁴+3x³+5x²  Find d⁴y/dx⁴

f^IIII(x)= 96

500

y=2x⁵+2x³+3x²  Find d⁴y/dx⁴

f^IIII(x)=240x

Limits

100

Lim x→2-  

 1/x² -4 

-∞

200

Lim x→2+  

 3/x-2        

∞

300

Lim x→-1    

 x+1/x²-1

-1/2

400

Lim x→3+     

-x²/3x-9

-∞

500

Lim x→ -π/3    

sec(x)

2