Class 12 CBSE A.O.D Exercise 6.4
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.
Please Select
Q1. Show that the following functions are strictly increasing on R:
(i) f(x) =3x+17
(ii) f(x) = 7x -3.
Solution :
Q2. (i) Show that the function f given by f(x) = 3 - 7x is strictly decreasing.
(ii) Show that the function f(x) = 1 - 1/x is strictly increasing.
Solution :
Q3.
(i) Prove that the function f(x) =3 + 1/x is strictly decreasing.
(ii) Show that the function f(x) =x- 1/x is strictly increasing.
Solution :
Q4.(i) Show that the function f(x) =e-2x is strictly decreasing on R.
(ii) Show that the function f(x) = 5x is strictly increasing.
(iii) Show that the function f(x) = log x is strictly increasing.
Solution :
Q5. For what value of k, the function f (x) = kx^3+ 5 is decreasing?
Solution :
Q6. Prove that the function f(x) = ax+b is strictly decreasing iff a>0
Solution :
Q7. Prove that the function f(x) = x3 – 6x2 + 12x – 18 is increasing on R.
Solution :
Q8. Show that the function f(x) = 4x3-18x2+27x-7 is increasing on R
Solution :
Q9. Prove that the function f(x)=5-3x+3x2-x3 is decreasing on R.
Solution :
Q10. Determine whether the following functions are increasing or decreasing for the
stated values
of x:
(i) f(x)=1/x,x< 0
(ii) f(x) = 1/1+x2,x ≥ 0
Solution :
Q11. Prove that the following functions are neither increasing nor decreasing
(i) f(x) =x2-x+1 on (-1,1)
(ii) f(x) = 1/x2 +1 on R
Solution :
Q12. Prove that the function f(x)= |x| is
(i) strictly increasing in (0, ∞)
(i) strictly decreasing in (—∞, 0).
Solution :
Q13. Find the intervals in which the following functions are strictly increasing
decreasing:
Solution :
Q14. Find the interval in which the function f(x) = x²e-x is increasing.
Solution :
Q15. Find the intervals in which the function given by f(x) = x2ex is strictly increasing or strictly decreasing.
Solution :
Q16. Find the intervals in which the function f(x) = 2 log (x-2)-x2+4x-5 is strictly increasing or strictly decreasing.
Solution :
