# Worksheet: Definition of the Derivative

Q1:

Using the definition of a derivative, evaluate .

• A
• B
• C
• D

Q2:

Let If is differentiable at , find and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q3:

Find if .

• A
• B
• C
• D

Q4:

Differentiate , and identify the value of at which the function is not differentiable.

• A , and the function is not differentiable at .
• B , and the function is not differentiable at .
• C , and the function is not differentiable at .
• D , and the function is not differentiable at .

Q5:

Differentiate , and identify the value of at which the function is not differentiable.

• A , and the function is not differentiable at .
• B , and the function is not differentiable at .
• C , and the function is not differentiable at .
• D , and the function is not differentiable at .

Q6:

Suppose What can be said of the differentiability of at ?

• AThe function is not differentiable at because is discontinuous at .
• BThe function is continuous but not differentiable at because .
• CThe function is differentiable at as but is not continuous.
• DThe function is differentiable at .
• EThe function is not differentiable at because is undefined.

Q7:

Find the derivative of the function using the definition of derivative, and then state the domain of the function and the domain of its derivative.

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q8:

Let . Use the definition of derivative to determine .

• A
• B
• C
• D

Q9:

Find the derivative of the function using the definition of derivative, and then state the domain of the function and the domain of its derivative.

• A , ,
• B , ,
• C , ,
• D , ,
• E , ,

Q10:

Differentiate , and identify the value of at which the function is not differentiable.

• A , and the function is not differentiable at .
• B , and the function is not differentiable at .
• C , and the function is not differentiable at .
• D , and the function is not differentiable at .