# Worksheet: Determing Whether a Function is Diffrentiable or Not

Q1:

Suppose What can be said of the differentiability of at ?

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

Q2:

Suppose What can be said of the differentiability of at ?

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

Q3:

Suppose What can be said of the differentiability of at ?

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

Q4:

Discuss the continuity and differentiability of the function at given

• AThe function is continuous but not differentiable at .
• BThe function is continuous and differentiable at .
• CThe function is not continuous, so it is not differentiable at .
• DThe function is not continuous but differentiable at .

Q5:

Discuss the differentiability of a function at given

• A is differentiable at because .
• B is not differentiable at because .
• C is not differentiable at because is undefined.
• D is differentiable at because is continuous at .

Q6:

Discuss the differentiability of the function at given .

• AThe function is differentiable at as is continuous at that point.
• BThe function is differentiable at that point as .
• CThe function is not differentiable at as is discontinuous at that point.
• DThe function is not differentiable at that point as .

Q7:

Discuss the differentiability of the function at given

• A is discontinuous but differentiable at because .
• B is not differentiable at because is undefined.
• C is differentiable at .
• D is not differentiable at because is discontinuous at .
• E is continuous but not differentiable at because .

Q8:

Suppose What can be said of the differentiability of at ?

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

Q9:

Suppose What can be said of the differentiability of at ?

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

Q10:

What can be said of the differentiability of at ?

• A is not differentiable at because is undefined.
• B is continuous but not differentiable at because .
• C is differentiable at .
• D is not differentiable at because is discontinuous at that point.

Q11:

Discuss the differentiability of the function at .

• AThe function is differentiable at because exists.
• BThe function is differentiable at because exists.
• CThe function is not differentiable at because does not exist.
• DThe function is not differentiable at because is not continuous at that point.

Q12:

Let If is differentiable at , find and .

• A,
• B,
• C,
• D,
• E,

Q13:

Let Determine the values of and so that is continuous at . What can be said of the differentiability of at this point?

• A, , not differentiable at
• B, , not differentiable at
• C, , differentiable at
• D, , differentiable at

Q14:

Let If and is continuous at , determine the values of and . What can be said of the differentiability of at this point?

• A, , not differentiable at
• B, , not differentiable at
• C, , differentiable at
• D, , differentiable at

Q15:

Find the values of and given the function is differentiable at where