Theorems

IVT

100

What conditions must be met to use the intermediate value theorem?

Continuous on a closed interval

200

Can the intermediate value theorem be used on the function (x²-4x-4)/(x-2) on the interval [0,5]. Justify your answer.

No, because there is an infinite discontinuity at x=2

300

Can the I.V.T be used to guarantee at some point f(c)=6 on the interval [-2,2] of the function x³-2. What, c value makes f(x)=6

Yes. c=2. 

400

Lucas Berman is 6 feet tall. At what point in time was he 73 inches tall?

Never. 6 feet is 72 inches.

500

dy/dx=-6x+6

y(0)=4

On the interval [0,4] will Y ever equal -20. What X value (if any exists) will make this true? 

Yes, x=4

EVT

100

Find the absolute maximum of f(x)=x² on the interval [1,3]

Absolute maximum at (3,9)

200

Find the coordinates of the absolute minimum of x²+1 on the interval [-2,2]

(0,1)

300

Find the coordinates of the absolute maximum on the interval [-3,3] of the function x²+2x+1

(3,16)

400

Find the absolute minimum of (x+4)/(2x²+x+8) on [-10,0]

x=-4±3√2

500

Determine the coordinates of the absolute extrema of y=ln(x²+4x+14) on [-4,2]

Absolute Maximum: 3.2581 at x=2

Absolute Minimum: 2.3026 at x=−2

MVT

100

Determine the values of c that satisfy the M.V.T of f(x)=2t−t²−t³ on the interval [-2,1] (calc active)

c=−1.215, 0.549

200

Determine the values of c which satisfy the MVT of f(x)=-8t+e^-3t on [-2,3] (Calc Active)

c=-1.0973

300

Determine the values of c that satisfy the M.V.T of f(x)=x²-2x-8 on the interval [-1,3]

c=1

400

Determine the values of c that satisfy the M.V.T of f(x)=(x²-6x+7)/(x-2)on the interval [0,4] (calc active)

The function is not continuous on the interval. Therefore no such C value can exist.

500

Determine the values of c that satisfy the M.V.T of f(x)=(x-4)/(x²+2) on the interval [0,4] (calc active)

c=0, c=1.759

Wild Card

100

What is the derivative of y=sin(8x³+4)

dy/dx=24x²cos(8x³+4)

200

Using implicit differentiation, solve for dy/dx

-x² +y³ = 4

dy/dx = -2x/3y²

400

Name three mathematicians who have Calculus concepts/theorems/methods named after them. (Last name)

Euler, Leibniz, Newton, L'hospital.

500

A light is mounted on a wall 5 meters above the ground. A 2 meter tall person is initially 10 meters from the wall and is moving towards the wall at a rate of 0.5 m/sec. After 4 seconds of moving is the tip of the shadow moving towards or away from the person and at what rate?

The tip of the shadow is moving towards the person at a rate of 1/3 m/s?

Class Trivia

100

What fine arts class is Vaghul in?

orchestra

200

Who usually wears scrubs?

Sai

300

What kind of cup does Arham usually bring?

Black/Stainless Travel Coffee

400

What position does Archit play in football? 

Safety

500

Name all classes Mrs. Hasten has taught at IHS.

Geometry OL, Precal OL, Pre-AP Precal, Precal Adv, Stats OL, AP Stats, AP Calc BC, AcDec