Calculus Concepts: Rates and Approximations

A balloon is rising vertically at a rate of 5 m/s. A boy is cycling along a straight road at a speed of 10 m/s. When the boy is directly under the balloon, the balloon is 20 meters above the ground. How fast is the distance between the boy and the balloon increasing at that moment?

• 10 m/s

• 11 m/s

• 12 m/s

• 13 m/s

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

• 5.01

• 5.005

• 5.1

• 5.05

Tags

CCSS.HSF.IF.B.6

• 2

• 2.5

• 3

• 3.5

Which of the following graphs represents a function with a derivative that is always positive?

• A line with a positive slope

• A parabola opening downwards

• A horizontal line

• A sine wave

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

• 5

• 6

• 7

• 8

A ladder 10 meters long is leaning against a wall. If the bottom of the ladder slides away from the wall at a rate of 1 m/s, how fast is the top of the ladder sliding down the wall when the bottom is 6 meters from the wall?

• 0.6 m/s

• 0.8 m/s

• 1.2 m/s

• 1.5 m/s

Tags

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

• 0.5

• 1

• 1.5

• 2

• 1

• 0

• 1.1

• 1.105

• 1.11

• 1.115

Tags

CCSS.HSF.IF.B.6

CCSS.HSF.IF.A.2