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Worksheet: Determining Whether a Function Is Differentiable

Q1:

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.

Q2:

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.

Q3:

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.

Q4:

Discuss the continuity and differentiability of the function at given

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

Q5:

Discuss the differentiability of a function at given

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

Q6:

Discuss the differentiability of the function at given .

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

Q7:

Discuss the differentiability of the function at given

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

Q8:

Suppose What can be said of the differentiability of at ?

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

Q9:

Suppose What can be said of the differentiability of at ?

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

Q10:

What can be said of the differentiability of at ?

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

Q11:

Discuss the differentiability of the function at .

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

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

Q15:

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