A.O.D-Rate of change of quantities.

If a function has a derivative that is negative, what does that tell you?

• The function is increasing

• The function is decreasing

• The function is constant

• Neither increasing nor decreasing

The radius of a circle is decreasing at a constant rate of 0.1 cm/sec.  In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

• -(0.2)πC
• -(0.1)C
• (0.1)²C
• (0.1)²C

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.4

CCSS.HSA.SSE.A.1

CCSS.HSA.SSE.B.3

If the base b of a triangle is increasing at a rate of 3 inches per minute while its height h is decreasing at a rate of 3 inches per minute, which of the following must be true about the area A of the triangle?

• A is always increasing
• A is always decreasing
• A is decreasing only when b < h
• A is decreasing only when b > h

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

The radius of a circle is increasing at a constant rate of 0.2 meters per second.  What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 20π meters?

• 0.04π m²/sec
• 0.4π m²/sec
• 4π m²/sec
• 20π m²/sec

Tags

CCSS.HSA.SSE.A.1

The radius of a sphere is decreasing at a rate of 2 cm/sec.  At the instant when the radius of the sphere is 3 cm, what is the rate of change, in cm²/sec, of the surface area of the sphere?  (The surface area of a sphere is A = 4πr².)

• -108π
• -72π
• -48π
• -24π

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

Which of the following functions does not satisfy the conditions put forth in Rolle's Theorem?

• $f\left(x\right)\ =\ \left(x-2\right)^{\frac{2}{3}}\$ on $\left[3,5\right]$

• $f\left(x\right)\ =\ \sqrt{1-x^2}$ on $\left[-1,1\right]$

• $f\left(x\right)=\left(2x-3\right)^4$ on $\left[1,2\right]$

• $f\left(x\right)=e^{-x^2}$ on $\left[-4,4\right]$

A function is decreasing if its first derivative is what?

• positive

• negative

• zero

• undefined

A function is increasing if its first derivative is what?

• undefined

• positive

• negative

• zero

The radius r of a sphere is increasing at a rate of 2 inches per minute.  Find the rate of change of the volume when r=6 inches.

• C=2πr
• A=πr²
• V=(4/3)πr³
• S=4πr²

Tags

CCSS.HSG.GMD.A.3

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Tags

CCSS.7.G.B.4