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Teacher:	Prof. JM	Section:	AS Mathematics Grade 11
Date:	Week	Grade	Grade 11

Application of Differentiation

Learning Objectives		Understand the concept of differentiation and how it relates to the rate of change of a function. Learn how to apply basic differentiation rules such as the power rule, sum rule, and constant rule to differentiate polynomials. Practice differentiating a variety of functions, including those with multiple terms and powers, to build fluency in differentiation techniques.
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Student Materials: Name:.......................Grade.................... Tangents and Normals Worksheet: Finding the Equation of the Tangent and Normal to a Curve at a Given Point Question 1: Find the equation of the tangent to the curve \( y = 3x^2 + 2x - 1 \) at the point where \( x = 1 \). Question 2: Find the equation of the tangent to the curve \( y = x^3 - 4x + 2 \) at the point where \( x = 2 \). Question 3: Find the equation of the tangent to the curve \( y = 5x^4 - 3x^2 + 7 \) at the point where \( x = -1 \). Question 4: Find the equation of the tangent to the curve \( y = 2x^2 - 6x + 4 \) at the point where \( x = 3 \). Question 5: Find the equation of the tangent to the curve \( y = x^2 + 2x - 5 \) at the point where \( x = -2 \). Question 6: Find the equation of the normal to the curve \( y = 3x^3 - x^2 + x - 2 \) at the point where \( x = 0 \). Question 7: Find the equation of the normal to the curve \( y = 4x^2 - 3x + 5 \) at the point where \( x = 1 \). Question 8: Find the equation of the normal to the curve \( y = 7x^3 - 2x + 1 \) at the point where \( x = -1 \). Question 9: Find the equation of the normal to the curve \( y = 6x^2 - 4x + 3 \) at the point where \( x = 0 \). Question 10: Find the equation of the normal to the curve \( y = 5x^2 - 7x + 2 \) at the point where \( x = 4 \). Answer Keys: Answer 1: \( y = 8x - 5 \) Answer 2: \( y = 10x - 16 \) Answer 3: \( y = -11x - 6 \) Answer 4: \( y = 6x - 10 \) Answer 5: \( y = -4x - 1 \) Answer 6: \( y = -2x - 2 \) Answer 7: \( y = -5x + 6 \) Answer 8: \( y = -13x + 10 \) Answer 9: \( y = -4x + 3 \) Answer 10: \( y = -29x + 122 \)	Student Materials: Show detailed steps here
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Student Materials:

Name:.......................Grade....................

Tangents and Normals

Worksheet: Finding the Equation of the Tangent and Normal to a Curve at a Given Point

Question 1: Find the equation of the tangent to the curve \( y = 3x^2 + 2x - 1 \) at the point where \( x = 1 \).

Question 2: Find the equation of the tangent to the curve \( y = x^3 - 4x + 2 \) at the point where \( x = 2 \).

Question 3: Find the equation of the tangent to the curve \( y = 5x^4 - 3x^2 + 7 \) at the point where \( x = -1 \).

Question 4: Find the equation of the tangent to the curve \( y = 2x^2 - 6x + 4 \) at the point where \( x = 3 \).

Question 5: Find the equation of the tangent to the curve \( y = x^2 + 2x - 5 \) at the point where \( x = -2 \).

Question 6: Find the equation of the normal to the curve \( y = 3x^3 - x^2 + x - 2 \) at the point where \( x = 0 \).

Question 7: Find the equation of the normal to the curve \( y = 4x^2 - 3x + 5 \) at the point where \( x = 1 \).

Question 8: Find the equation of the normal to the curve \( y = 7x^3 - 2x + 1 \) at the point where \( x = -1 \).

Question 9: Find the equation of the normal to the curve \( y = 6x^2 - 4x + 3 \) at the point where \( x = 0 \).

Question 10: Find the equation of the normal to the curve \( y = 5x^2 - 7x + 2 \) at the point where \( x = 4 \).

Answer Keys:

Answer 1: \( y = 8x - 5 \)
Answer 2: \( y = 10x - 16 \)
Answer 3: \( y = -11x - 6 \)
Answer 4: \( y = 6x - 10 \)
Answer 5: \( y = -4x - 1 \)
Answer 6: \( y = -2x - 2 \)
Answer 7: \( y = -5x + 6 \)
Answer 8: \( y = -13x + 10 \)
Answer 9: \( y = -4x + 3 \)
Answer 10: \( y = -29x + 122 \)