AROC-IROC-Derivative.

When you plug a given value into the derivative of a function, you get this. Select all that apply.

• tangent line

• instantaneous rate of change

• slope

• average rate of change

Superman has a displacement function of 
 $f\left(t\right)=t^2+3$  
where f (t) is how far Superman has gone in miles after t minutes. What is his average rate of change during the first 4 minutes?

• 3 miles/minute

• 4 miles/min

• 0.25 miles/minute

• 4.75 miles/min

• none of these

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

This is a line that touches the function at a given point and has a slope that is equal to the instantaneous rate of change at a given point.

• normal line

• tangent line

• delta line

• secant line

Given f(x) passes through the point (8, 21) and

f ' (x) =2x - 7, write the equation of the tangent line.

• $y=2x+8$

• $y=2\left(x-8\right)+21$

• $y=9\left(x-8\right)+21$

• $y=9x+21$

• not enough information to tell

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Given the graph of f (x),

What can you tell about f ' (5)?

NOTE: Click on the graph if you need to see it larger.

• it's positive

• it's negative

• it does not exist

• nothing

Tags

CCSS.HSF.IF.A.2

The table above represents the function h(x). Based on the given information, what is the best approximation we can make for h'(22)?

• 160

• 15

• 3.5

• 3

• $\frac{1}{3}$

Tags

CCSS.HSF.IF.B.4

Write the equation of the line tangent to the graph of f (x) given f(5) = 6 and the graph of its derivative, f ' (x), as shown.

• y = 5x - 19

• y = 10x - 44

• y = 10x + 6

• y = 5x - 6

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Condense: $3\ln x\ +\ 4\ln3$  

•  $\ln\left(x^3+81\right)$  

•  $\ln\left(3x+81\right)$  

•  $\ln\left(81x^3\right)$  

•  $\ln\left(12x\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand:  $\ln\left(x-1\right)^3$  

•  $3\ln x-3\ln1$  

•  $3\ln\left(x-1\right)$  

•  $\ln x^3-\ln1$  

• Cannot be expanded

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Evaluate if possible: $\frac{\ln e^5}{\ln\left(\frac{1}{e}\right)}$  

• 5

• e

• -5

• 0

• Undefined

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4