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

https://youtu.be/r665nuJbB2I
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  https://youtu.be/r665nuJbB2I?si=aEZ0xqqqVbThgMYP
Logarithms  https://youtu.be/SZxARGQvAdM?si=YLJiLJYO1umZcyem
Integration  https://youtu.be/2BMaVP7X-78?si=0HSbPS1t3Pzy-IQT
Formulas Sheet (use laptop)  https://youtu.be/pPjMzG1xygM?si=nFJHWQcJWEcQK8V4

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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Class 12 ex 3.1 solution
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