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Class 12 Maths Exercise 3.1 New KPK Book | Class 12 Maths Ex 3.1 KPK Book | FBISE Differentiation

   • Class 12 Maths Differentiation (Calculus) ...  
Calculus Summarized One Shot Video of 40 Minutes
(This video is crux of Differentiation and Integration. Must go through this video by pausing and thinking , if you are a slow learner. Must see this video twice atleast, on consecutive week ends.)

Differentiation     • Class 12 Maths Differentiation (Calculus) ...  
Logarithms     • Exponents, Logarithms and their derivative...  
Integration     • Class 12 Maths Integration One Shot Video ...  
Formulas Sheet (use laptop)     • Complete Formulas of Class 12 Maths KPK Bo...  

00:00 Q1
16:10 Q2
28:50 Q3
33:49 Q4
37:42 Q5
42:40 Q6
57:05 Q7
01:04:00 Q8

1. Find the average rate of change of the following functions over the indicated intervals.
a. y = x2 + 4 from x=2 to x=3
b. y = x2 + x/3 from x=-3 to x=3
c. s = 2t3 – 5t + 7 from t=1 to t=3
d. h = 2t + 4 from t=8 to t=8.5

2. Use definition for the rate of change to find out the average rate of change over the specified interval for the following functions
a. s = 2t - 3 from t=2 to t=5
b. y = x2 – 6x + 8 from x=3 to x=3.1
c. A = r2 from r=2 to r=2.1
d. h = t - 9 from t=9 to t=16

3. A ball is thrown straight up. Its height after t seconds is given by the formula h=-16t2 + 80t. Use definition to determine the average velocity for the specified intervals.
a. From (t = 2 to t = 2.1)
b. From (t = 2 to t = 2.01)
4. The rate of change of price is called ‘Inflation’. The price ‘P’ in rupees after ‘t’ years is P(t)=3t2 +t +1. Use definition for the rate of change to determine the average rate of change of inflation for t=3 to t=5 years. What the rate of change means?

5. A farmer plants x acres of sugar beets. The profit generated is f(x) = 1800x – 9x2. Determine the average rate of change of the profit when planted area is between x=20 acres and x=50 acres. What the rate of change mean, explain?

6. Use first principle rule to determine the derivative of the following functions.
a. f(x) = 3x
b. f(x) = (5x + 6)1/2
c. f(x) = x2 + 1
d. f(x) = 12 - x2
e. f(x) = 16x2 - 7x
f. f(x) = 7/x

7. Use function f(x) = x2 - 7x + 6 to do the following functions.
a. Find the derivative of a function at point P (5,-4)
b. Find the tangent line on the curve y=x2 - 7x + 6 at point P (5,-4)
c. View the slope of the tangent line on the curve at point P (6, 0)

8. Use definition of derivative to determine slope of the tangent line to the curve at a given point and then find out the tangent line equation on that curve at the same point, for the following curves.
a. f(x) = -x2 +7x , x =3
b. f(x) = 6x2 -11x -10 , x =1
c. f(x) = -3x2 -6x -10, x =0
d. f(x) = 2x2 +3x -4 , x =1

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