BC 5.6 Mixed Practice

Derivatives

200

Find the derivative of x²+4x+3

What is 2x+4?

400

Find the derivative of -x³+4x²-5

What is -3x²+8x?

600

Find the second derivative of f(x)=sin(2x³-9x)

What is 12cosx(2x³-9x)-(6x²-9)²sin(2x³-9x)

800

Find the third derivative of f(x)=11x⁵-3x⁴+9x³+6x²

What is 660x²-72x+54?

1000

Find f'(3) when f(x)=(4x²+9)sin(7x³)

What is 7,457.258?

Antiderivatives

200

Find the antiderivative of 12-x

What is 12x-(x²/2)?

400

Find the antiderivative of 8x³-9x²+4

What is 2x⁴-3x³+4x?

600

Find the antiderivative of (√x)+(1/√x)

What is (2/3)x^3/2+x^1/2?

800

Find the antiderivative of (x²+2x-3)/x⁴

What is -(1/x)-(1/x²)+(1/x³)?

1000

Find the antiderivative of (3/t)-(7/t²)

What is 3ln|t|+(2/t)?

Wild Card

200

Solve this limit using variables: Lim_x→a C = 

What is C?

(Constant rule)

400

This theorem states "if f is a differentiable function on the interval [a,b], then there exists a number c between a and b such that f'(c)=[f(b)-f(a)]/(b-a)."

What is the Mean Value Theorem?

600

Why do they only serve food and no drinks at a calculus party?

Because you can't drink and derive

800

What do you call guys that love math?

Algebros

1000

This theorem states "if f is continuous on a closed interval [a,b], then f attains an absolute maximum value."

What is the Extreme Value Theorem?

More Antiderivatives!

200

-sin x + C

What is the antiderivative of -cos x?

400

2 ln x + C

What is the antiderivative of 2/x?

600

secx tanx + C

What is the antiderivative of sec x?

800

-(1/2) cos(2x) + C

What is the antiderivative of sin(2x)?

1000

cot x + C

What is the antiderivative of -csc2x?