AP Calc Unit 2 Derivatives Review

Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn (cusp) in the first quadrant so it is not differentiable at that x value.

• No, the function is discontinuous so it is not differentiable.

Tags

CCSS.HSA.REI.C.7

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Tags

CCSS.8.F.A.3

Is the above function differentiable at

x = 0? Why?

• Yes. The derivative would be equal to zero since there is a vertical tangent.

• No. The derivative would not exist at x = 0 since there is a vertical tangent.

The derivative of a function is its

• Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator

• 0

• 1

• 2

• 3

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

f'(x)=

• an equation for the slope of the tangent line

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• 10

• DNE

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

• True

• False

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

• corner, cusp, horizontal tangent, discontinuity
• corner, cusp, vertical tangent, continuity
• corner, cusp, vertical tangent, discontinuity
• corner, curve, vertical tangent, continuity

• Average Rate of Change
• Average Value of f
• Intermediate Value Theorem
• Rolle's Theorem

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6