Applications of Derivatives Review

The function f is twice differentiable with f(2) = 1, f'(2)=4, and f''(2)=3.  What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x = 2?

• 0.4
• 0.6
• 0.7
• 1.4

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Suppose that for a twice differentiable function f (x), f '(x) > 0 and f ''(x) > 0 on the interval (1,3). If we use a linear approximation at x = 2 to estimate f (1.9), will that estimate be an underestimate or overestimate, and why?

• Underestimate since f '' > 0 on (1, 3)

• Overestimate since f '' > 0 on (1,3)

• Underestimate since f ' > 0 on (1, 3)

• Overestimate since f ' > 0 on (1, 3)

A railroad track and a road cross at right angles.  An observer stands on the road 70 meters south of the crossing and watches an eastbound train traveling at 60 meters per second.  At how many meters per second is the train moving away from the observer 4 seconds after it passes through the intersection?

• 57.60
• 57.88
• 59.20
• 67.40

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

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

The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle whose velocity is given by v(t) = t³ - 3t² + 12t + 4 is

• 9
• 12
• 14
• 21

A rectangular solid that has a square base has a surface area of 150 square inches.  Find the maximum volume of the solid.  (use Calculus)

• 5
• 125
• 150
• 250

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Suppose that the sides of a square increase from 3 cm to 3.3 cm. Estimate the change in the area of the square.

• 1.8 cm²

• 1.89 cm²

• 0.9 cm²

• 19.8 cm²

Tags

CCSS.HSG.MG.A.1