Limits, Derivatives, and Functions, Oh My!

From the table, determine if a limit exists at 2 and, if so, what is it?

• yes the limit exists; .8

• no the limit does not exist

• yes the limit exists; 2

• yes the limit exits; 8

Find the limit as x approaches 1.

• 0

• 3

• DNE

• ∞

Tags

CCSS.HSF.IF.A.2

What three conditions must exist for a function to be continuous?

• ƒ(c) must exist

• the limit as x → c must exist

• the limit as x →c must equal ƒ(c)

• all functions are continuous

Tags

CCSS.HSF-IF.C.7D

Find the limit.

• 0

• DNE

• 6/5

• 15

Find the limit.

• 1/8

• 8

• -1/8

• DNE

For what values of x does f(x) have a horizontal tangent?

• -3.5, 3.5

• -5, 5

• there are no horizontal tangents

• -5, 0, 5

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.11

According to the graph, at the point x=-2, is f(x) increasing or decreasing and why?

• At x=-2 f(x) is increasing because the graph has a positive slope.

• At x=-2 f(x) is decreasing because the graph has a positive slope.

• At x=-2 f(x) is decreasing because the graph lies below the x-axis.

• At x=-2 f(x) is decreasing because the graph has a negative slope

Tags

CCSS.HSF.IF.B.4

Order the derivatives of each point on the graph from least to greatest.

• ABC

• BCA

• CBA

• BAC

Tags

CCSS.HSS.ID.C.7

If f(x)=x²+3x and f'(x)=2x+3, find the value of x where f(x) has a horizontal tangent.

• -3

• -3/2

• 2/3

• 0

Differentiate f(x)=x+√x

• f'(x)=x+1

• f'(x)=1+1/√x

• f'(x)=1+1/2

• f'(x)=1+(1/2√x)