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Worksheet: An Introduction to the Definition of the Derivative

Q1:

If the function , find .

  • A
  • B
  • C
  • D
  • E

Q2:

If the function , find .

  • A
  • B
  • C
  • D9
  • E

Q3:

If the function , find .

  • A
  • B
  • C
  • D12
  • E

Q4:

If the function , find .

  • A
  • B
  • C
  • D4
  • E

Q5:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

  • A, the gradient of the tangent at point
  • B, the gradient of the tangent at point
  • C, the gradient of the tangent at point
  • D, the gradient of the tangent at point
  • E, the gradient of the tangent at point

Q6:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

  • A, the gradient of the tangent at point
  • B, the gradient of the tangent at point
  • C, the gradient of the tangent at point
  • D, the gradient of the tangent at point
  • E, the gradient of the tangent at point

Q7:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

  • A, the gradient of the tangent at point
  • B, the gradient of the tangent at point
  • C, the gradient of the tangent at point
  • D, the gradient of the tangent at point

Q8:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

  • A, the gradient of the tangent at point
  • B, the gradient of the tangent at point
  • C, the gradient of the tangent at point
  • D, the gradient of the tangent at point

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:

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, ,

Q11:

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, ,

Q12:

Let . Use the definition of derivative to determine . What is the gradient of the tangent to its graph at ?

  • A, the gradient of the tangent at point
  • B, the gradient of the tangent at point
  • C, the gradient of the tangent at point
  • D, the gradient of the tangent at point

Q13:

Let . Use the definition of the derivative to determine .

  • A
  • B
  • C
  • D

Q14:

Determine the derivative of the function using the definition of the derivative.

  • A
  • B
  • C
  • D

Q15:

Evaluate .

  • A
  • B
  • C
  • D
  • E

Q16:

Evaluate .

  • A
  • B
  • C
  • D
  • E