Calculus Review 3.1-3.3

Use the definition of the derivative (aka the limit process) to find the derivative of y=x^2+9 (be ready to show work on the test).

• x^2

• 2x+9

• 2

• 2x

This is NOT a correct notation for a derivative

• y ' (say it as "y prime")

• f '(x) (say it as "f prime of x")

• dy/dx

• dx/dy

It's the average rate of change of f(x)=1/(x+4) on the interval [-3, 0].

• 0

• -1/2

• -1/4

• -1

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Which is NOT a term for slope?

• rate of change

• derivative

• rise over run

• tangent line

Tags

CCSS.8.EE.B.5

Write the equation of the line tangent to the graph of f(x) at the point (5, 6) given the graph of it's derivative, f ' (x), as shown.

• y = 5x - 15

• y = 10x - 44

• y = 10x - 6

• y = 5x - 8

Why is there no derivative at x = 6?

• the limit dne

• it's not locally linear

• it's not continuous

• there's a vertical tangent line

Why is there no derivative at x = 11?

• the limit dne

• it's not locally linear

• it's not continuous

• there's a vertical tangent line

Is the graph continuous everywhere on the interval (3, 10)?

• yes

• no

Tags

CCSS.HSF-IF.C.7B

Is the graph differentiable everywhere on the interval (3, 10)?

• yes

• no

Tags

CCSS.HSF-IF.C.7B

The function f is differentiable

• at a if f '(a) exists.

• at 0 if f '(x) exists.

• at a if f '(a) does not exists.

• at 0 if f '(x) does not exists.