Class 12 CBSE A.O.D Exercise 6.5

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 6.1 Exercise 6.2 Exercise 6.3 Exercise 6.4 Exercise 6.6 Exercise 6.7 Exercise 6.8 Exercise 6.9 Exercise 6.10 Case Study

Q1. Find the maximum and the minimum values (if any) of the following functions:

1. (i) f(x) = x²
(ii) f(x) = (2x-1)2 + 3.

Solution :



Q2. (i) f(x)=-(x-1)²+10

(ii) f(x)=9x2+12x + 2.

Solution :



Q3. (i) f(x) = |x|

(ii) f(x) = x3 +1.

Solution :



Q4. (i) f(x) = |x+2|-1

(ii) f(x)=3+ |x|

Solution :



Q5. Prove that the function f(x)=x3+x2+x+1 does not have maxima or minima

Solution :



Q6. Find the (absolute) maximum and the (absolute) minimum values of the following functions in the indicated intervals. Also find the points of (absolute) maxima and minima:

(i) f(x)=(x-1)2 + 3 in [-3, 1]
(ii) f(x)=2x3-15x2 + 36x + 1 on the interval [1, 5]
(iii) f(x)=3x4-8x3 + 12x²-48x + 25 in [0,3].

Solution :

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