Ncert Solutions Maths class 12th
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New answer posted
4 months agoContributor-Level 10
(a) f (x) = x2 + 2x - 5.
f(x) = 2x + 2 = 2 (x + 1).
At, f(x) = 0
2 (x + 1) = 0
x = -1.
At, x
f(x) = (- ) ve< 0.
So, f (x)is strictly decreasing or
At x ∈
f(x) = ( + ve) > 1
f(x) is strictly increasing on
(b) f(x) = 10 - 6x- 2x2
So, f(x) = - 6 - 4x = - 2 (3 + 2x).
Atf(x) = 0
2 (3 + 2x) = 0.
x =
At x
∴f(x) is strictly increasing on
At x
f(x) = ( -ve) ( + ve) = ( - ) ve< 0.
∴f (x) is strictly decreasing on
(c) f (x) = 2x3- 9x2- 12x.
So, f (x) =- 6x2- 18x- 12 = - 6 (x2 + 3x + 2).
= -6 [x2 + x + 2x + 2]
= -6 [x (x + 1) + 2 (x + 1)]
= -6 (x + 1) (x + 2)
At, f (x) = 0.
6 (x + 1) (x + 2) = 0
x = -1 and x =
New answer posted
4 months agoContributor-Level 10
We have, f (x) = 2x3- 3x2- 36x + 7.
So, f (x) =
= 6 (x2-x- 6).
= 6 (x2- 3x + 2x- 6)
= 6 [x (x- 3) + 2 (x- 3)]
= 6 (x- 3) (x + 2).
At, f (x) = 0
6 (x- 3) (x + 2) = 0.
So, when x- 3 = 0 or x + 2 = 0.
x = 3 or x = -2.
Hence we an divide the real line into three disjoint internal
I
At x ∈
f (x) = ( + ve) ( -ve) ( -ve) = ( + ve) > 0.
So, f (x) is strictly increasing in
At, x∈ ( -2,3),
f (x) = ( + ve) ( + ve) ( -ve) = ( -ve) < 0.
So, f (x) is strictly decreasing in ( -2,3).
At, x ∈
f (x) = ( + ve) ( + ve) ( + ve) = ( + )ve> 0.
So, f (x) is strictly increasing in
∴ (a) f (x) is strictly increasing in
(b) f (x) is strictly decr
New answer posted
4 months agoContributor-Level 10
We have, f (x) = 2x2 3x
So, f (x) =
Atf (x) = 0.
4x - 3 = 0
i e, divides the real line into two
disjoint interval
(a) Now,
f (x) = 4x - 3 > 0
So, f (x) is strictly increasing in
(b) Now, f (x) = 4x - 3 < 0
So, f (x) is strictly decreasing in
New answer posted
4 months agoContributor-Level 10
We have, f (x) = sin x.
So, f (x) = cosx.
(a) when, x ∈ i e, x in 1st quadrat.
f (x) = cos.x> 0
f (x) is strictly increasing in .
(b) when, x ∈ in IInd quadrat
f (x) = cosx< 0.
∴f (x) is strictly decreasing (π
(c) When, x ∈ (0, π).
f (x) = cosx is increasing in and decreasing
in and f = cos
∴f (x) is neither increasing not decreasing in (0, π).
New answer posted
4 months agoContributor-Level 10
We have, f (x) = e2x
So, f (x) = = = 2e2x> 0
∴f (x) is strictly increasing on R.
New answer posted
4 months agoContributor-Level 10
We have, .
f (x) = 3x + 17.
So, f (x) = 3 > 0
∴f (x) is strictly increasing on R.
New answer posted
4 months agoContributor-Level 10
Given, R (x) = 3x2 + 36x + 5.
Marginal revenue,
= 3 * 2x + 36
= 6x + 36
When x = 15.
= 90 + 36 = 126
Option (D) is correct.
New answer posted
4 months agoContributor-Level 10
The area A of the isle with radius r is given by with respect to radius r A = πr2.
Then, rate of change of area of the circle
= 2πr.
When r = 6 cm
Q option (B) is correct.
New answer posted
4 months agoContributor-Level 10
Given, R (x) = 13x2 + 26x + 15.
Marginal revenue is the rate of change of total revenue with respect to the number of units sold Marginal revenue (MR) =
= 13 * 2x + 26
= 26x + 26
When x = 7,
MR = 26 * 7 + 26 = 182 + 26 = 208.
Hence, the required marginal reverse = ' 208.
Choose the correct answer for questions 17 and 18.
New answer posted
4 months agoContributor-Level 10
Given, c (x) = 0.007 x3- 0.003x2 + 15x + 400.
Since the marginal cost is the rate of change of total cost wrt the output we have,
Marginal cost, MC, =
= 0.007 * 3x2- 0.003 * 2x + 15.
When x = 17,
Then, MC = 0.007 * 2. (17)2 - 0.003 2 (17) + 15.
= 6.069 - 0.102 + 15.
= 20.967
Hence, the required marginal cost = ' 20, 97.
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