Applications of Derivatives

Given the position function, find the velocity at t=7

• 10
• 6
• 11
• 1

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

Given the position function, find the acceleration at t=8

• -2
• 1
• 2
• 3

A particle moves in a straight line with a velocity of v(t) = 2t². How far does the particle move between times t = 1 and t = 3?

• 18

• 52/3

• 26/3

• 16

For times t > 0, a particle moves on the x axis with its acceleration defined by a(t) = 6t – 2. If the velocity of the particle is -7 at t = 1, then at what time is the particle at rest?

• t = 4

• t = 1

• t = 2

• t = 4/3

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

A particle moves along the x axis with its acceleration given by a(t) = t² – 2t for 0 < t < 6. At time t = 0, the velocity is 10. What is the maximum velocity of this particle on the specified interval?

• 10

• 26

• 40

• 46

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

You want to make a box to contain dirt and your pet earthworm. Using a 7 in by 10 in rectangle of cardboard, you cut congruent squares from the corners and fold up the sides.

Choose the equation would you use in order to do Calculus to find the maximum volume of dirt (including worm) the box can hold?

• $V=\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-2x\right)\left(10-2x\right)$

• $V=x\left(7-x\right)\left(10-x\right)$

• $V=x\left(7+2x\right)\left(10+2x\right)$

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins. (see picture)

Choose the equation that represents this information.

• $2x+4y=32$

• $2x+2y=32$

• $xy=32$

• $A=3xy$

Tags

CCSS.HSA.CED.A.3

same question, but more ...
There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

Which equation represents the fence amount (F) that you want to minimize?

•  $F=2x+4y$ 

•  $F=2x+2y$ 

•  $F=xy$ 

•  $F=3\left(x+y\right)$ 

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

same question, now solve it and answer the question:

Farmer Jo has 32 square feet of land in which to make an enclosure for bunnies, chicks, and penguins.  There will be fencing put in around the entire enclosure and in the middle (as pictured) to create 3 sections, what dimensions should the overall enclosure be in order to use the least amount of fence?

• The overall enclosure should be 8 feet by 8 feet

• The overall enclosure should be 8 feet by 4 feet

• The overall enclosure should be 32 square feet

• The overall enclosure should be  $\sqrt{128}=8\sqrt{2}$  feet on each dimension

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.SSE.A.1

CCSS.HSG.MG.A.3

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem. 

•  $x^2=120$  and  $V=x^3$  

•  $2x+y=120$  and   $V=xy$  

•  $x^2y=120$  and  $V=2x^2+4xy$  

•  $2x^2+4xy=120$  and  $V=x^2y$  

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2