OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-11(a), Exe-11(b), Exe-11(c), Exe-11(d) and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Class:	12th
Subject:	Mathematics
Chapter  :	Ch-11 Applications of Derivatives  of Section -A

Board	ISC
Writer	OP Malhotra, SK Gupta, Anubhuti Gangal
Publications	S.Chand Publications 2020-21

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-: Included Topics :- 

Exe-11(a)

Exe-11(b)

Exe-11(c)

Exe-11(d)

Chapter Test

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OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Derivatives :-

Derivatives Maths refers to the instantaneous rate of change of a quantity with respect to the other. It helps to investigate the moment by moment nature of an amount.

Rate of change of quantity :-

Consider a function y = f(x), the rate of change of a function is defined as-

dy/dx = f'(x)

Further, if two variables x and y are varying to another variable, say if x = f(t), and y = g(t), then using Chain Rule :

dy/dx = (dy/dt)/(dx/dt)

where dx/dt is not equal to 0.

Increasing and Decreasing Functions :

Consider a function f, continuous in [a,b] and differentiable on the open interval (a,b), then

(i) f is increasing in [a,b] if f'(x)>0 for each x in (a,b)

(ii) f is decreasing in [a,b] if f'(x)< 0 for each x in (a,b)

(iii) f is constant function in [a,b], if  f'(x) = 0 for each x in (a,b)

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Exe-11(a)

OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Question 1:

Find the shape of the following curves :

………………..

…………………

Question 2:

Find the slope of the ………………………….. is 2 .

Question 3:

…………………..

……………………

……………………

Question 15:

The equation of tangent at (2, 3) on ……………..  the value of a and b.

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Exe-11(b)

 Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Question 1:

Using differential, find the approximate value of each of the following up to 3 place of decimal.

………………………

Question 2:

……………………..

…………………….

………………………

Question 9:

A closed circular cylinder has height 16 cm, and radius r cm. The total surface area is A cm²  Prove taha.

………..

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Exe-11(c)

OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Question 1:

If y² = 4x , find the rat/at which y is changing ………………  x = 4

Question 2:

If the radius …………… in the area.

Question 3:

………………….

………………….

…………………..

Question 18:

If the area of circle increases at a uniform ………………………. as the radius.

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First-Order Derivative :

The first order derivatives tell about the direction of the function whether the function is increasing or decreasing. The first derivative math or first-order derivative can be interpreted as an instantaneous rate of change. It can also be predicted from the slope of the tangent line.

Second-Order Derivative :

The second-order derivatives are used to get an idea of the shape of the graph for the given function. The functions can be classified in terms of concavity. The concavity of the given graph function is classified into two types namely.

Limit and Derivative :

When dx is made so small that is becoming almost nothing. With Limits, we mean to say that X approaches zero but does not become zero.

Mathematically: means for all real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |f(x) − L| < ε

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Exe-11(d)

OP Malhotra Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Question 1:

Show that the function f (x)  = ………………. (x ≠ 0).

Question 2:

Show that the function …………… increasing.

Question 3:

……………………..

…………………….

……………………….

Question 20:

Find the intervals in which the following function is increasing or decreasing :

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Chapter Test

Applications of Derivatives S.Chand ISC Class-12 Maths Solutions Ch-11

Question 1:

Find approximate  value of ……………. decimal places.

Question 2:

An edge of a various cube is increasing at the rate of ………………….. the edge is 5 cm long ?

Question 3:

……………………..

………………………

……………………..

Question 12:

Find the interval in which the ……………… increasing or decreasing.

-: End of Applications of Derivatives S. Chand ISC Class-12 Maths Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-12 Maths Solutions

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