RD Sharma Solutions for Class 12-science Maths CBSE Chapter 15: Mean Value Theorems

Mean Value Theorem
Mean Value Theorem

Class 12-science RD SHARMA Solutions Maths Chapter 15 – Mean Value Theorems

Mean Value Theorems Exercise Ex. 15.1

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 1(vi)

Solution 2(i)

Solution 2(iii)

Solution 2(iv)

Solution 2(v)

Solution 2(vi)

Solution 2(vii)

Solution 2(viii)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 3(v)

Solution 3(vi)

Solution 3(vii)

Here,

Solution 3(viii)

Solution 3(ix)

Solution 3(x)

Solution 3(xi)

Solution 3(xii)

Solution 3(xiii)

Solution 3(xiv)


Solution 3(xv)

Solution 3(xvi)

Solution 3(xvii)

Solution 3(xviii)

Solution 7

x = 0 then y = 16

Therefore, the point on the curve is (0, 16)

Solution 8(i)

x = 0, then y = 0

Therefore, the point is (0, 0)

Solution 8(ii)

Solution 8(iii)

x = 1/2, then y = – 27

Therefore, the point is (1/2, – 27)

Solution 9

Solution 10

Solution 11

Solution 2(ii)

Given function is

As the given function is a polynomial, so it is continuous and differentiable everywhere.

Let’s find the extreme values

Therefore, f(2) = f(6).

So, Rolle’s theorem is applicable for f on [2, 6].

Let’s find the derivative of f(x)

Take f'(x) = 0

As 4 ∈ [2, 6] and f'(4) = 0.

Thus, Rolle’s theorem is verified.

Mean Value Theorems Exercise Ex. 15.2

Solution 1(i)

Solution 1(ii)

Solution 1(iii)

Solution 1(iv)

Solution 1(v)

Solution 1(vi)

Solution 1(vii)

Solution 1(viii)

Solution 1(ix)

Solution 1(x)

Solution 1(xi)

Solution 1(xii)

Solution 1(xiii)

Solution 1(xiv)

Solution 1(xv)

Solution 1(xvi)

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

Mean Value Theorems Exercise MCQ

Solution 1

Correct option: (c)

Solution 2

Correct option: (c)

Solution 3

Correct option: (b)

Solution 4

Correct option: (c)

Using statement of Lagrange’s mean value theorem function is continuous on [a,b], differentiable on (a,b) then there exists c such that a < x1< b.

Solution 5

Correct option: (b)

ϕ(x) is continuous and differentiable function then using statement of Rolle’s theorem f(a)=f(b). Hence, here sin 0=0 also sin п=0. The answer is [0, ].

Solution 6

Correct option: (a)

Solution 7

Correct option: (a)

Solution 8

Correct answer: (c)

Solution 9

Correct option: (d)

Solution 10

Correct option: (a)

Solution 11

Correct option: (d)

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