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

Mean Value Theorems Exercise Ex. 15.1

Here,

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(iii)

x = 1/2, then y = - 27

Therefore, the point is (1/2, - 27)

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 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 9

Correct option: (d)

Solution 10

Correct option: (a)

Solution 11

Correct option: (d)