1. WELCOME TO THE HIGHER MATHEMATICS CLASS
SHIPAN CHANDRA DEBNATH ASSISTANT PROFESSOR & HEAD OF THE DEPARTMENT DEPARTMENT OF MATHEMATICS CHITTAGONG CANTONMENT PUBLIC COLLEGE

2. DIFFERENTIATION Today`s Topics is Chapter - 9 Exercise -9(D)
Book: Higher Mathematics
Axorpotra Publications

3. Learning Outcomes After complete this chapter students can
Apply Differentiation in different field
2 Find the Maximum and Minimum value

4. If y=mx+c is a straight line ,where m is a slope. Then 𝑑𝑦 𝑑𝑥 =𝑚 𝑖. 𝑒
If y=mx+c is a straight line ,where m is a slope. Then 𝑑𝑦 𝑑𝑥 =𝑚 𝑖.𝑒. 𝑠𝑙𝑜𝑝𝑒 𝑎𝑛𝑑 𝑑𝑦 𝑑𝑥 are the same
Therefore ,
1.The Equation of Tangent which passes through the point (x1,y1) becomes y-y1= 𝑑𝑦 𝑑𝑥 (x-x1)
2. The Equation of Normal which passes through the point (x1,y1) becomes y-y1=- 𝑑𝑥 𝑑𝑦 (x-x1)
3.If the tangents are parallel to x-axis then 𝑑𝑦 𝑑𝑥 =0
4. .If the tangents are parallel to y-axis i.e Perpendicular to x-axis then 𝑑𝑥 𝑑𝑦 =0
5. If the tangents makes equal angle with both axes then 𝑑𝑦 𝑑𝑥 =±1

5. CLASS WORK
1.Find the Equation of the tangents and normal of the curve y=x3-2x2+4 at the point (2,4)
2. Find the Equation of the tangents and normal of the curve y(x-2)(x-3)-x+7=0 which meet x-axis.
3. Find the value of slope of the curve x2+xy+y2=4 at the point (2,-2)
4. Find the co ordinate of the points of the curve y=x3-3x+2 where tangents are parallel to x-axis.
5. Find the co ordinate of the points of the curve y=x2+(1-x2) where tangents are parallel to y-axis.

6. EVALUATION
Tell me the First Principle of Derivative
why the derivative of constant is 0?

7. HOME WORK
1.Find the Equation of the tangents and normal of the curve y=x3-3x+2 at the point (2,-2)
2. Find the Equation of the tangents and normal of the curve y(x-1)(x-2)-x+3=0 which meet x-axis.
3. Find the value of slope of the curve y=(x+1)(x-1)(x-3) which meets x-axis.
4. Find the co ordinate of the points of the curve x2+y2-2x-3=0 where tangents are parallel to x-axis.
5. Find the co ordinate of the points of the curve y2=x2(a-x)where tangents are parallel to y-axis.

8. THANKS TO ALL,
DEAR STUDENT
Sir Issac Newton, Father of Calculus