RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 (Updated for 2021-22)

RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1 is mentioned in this article. The key topics covered in exercise 15.1 are Rolle’s theorem, the geometrical theorem of Rolle’s theorem of given functions, and illustrative examples. Our experts have created exercise-wise RD Sharma Class 12 Solutions with explanations for each step to make problem-solving easier for students. It allows them to assess their understanding of the concepts covered in this chapter. Students can utilise RD Sharma Solutions for Class 12 Maths Chapter 15 Mean Value Theorems Exercise 15.1 as reference materials to analyse Maths.

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RD Sharma Solutions Class 12 Maths Chapter 15 Exercise 15.1

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 15 – Mean Value Theorems Exercise 15.1 Important Questions With Solution

1. Discuss the applicability of Rolle’s Theorem for the following functions on the indicated intervals:

Solution:

(ii) f (x) = [x] for -1 ≤ x ≤ 1, where [x] denotes the greatest integer not exceeding x

Solution:

Solution:

(iv) f (x) = 2x² – 5x + 3 on [1, 3]

Solution:

Given function is f (x) = 2x² – 5x + 3 on [1, 3]

Since given function f is a polynomial. So, it is continuous and differentiable everywhere.

Now, we find the values of function at the extreme values.

⇒ f (1) = 2(1)²–5(1) + 3

⇒ f (1) = 2 – 5 + 3

⇒ f (1) = 0…… (1)

⇒ f (3) = 2(3)²–5(3) + 3

⇒ f (3) = 2(9)–15 + 3

⇒ f (3) = 18 – 12

⇒ f (3) = 6…… (2)

From (1) and (2), we can say that, f (1) ≠ f (3)

∴ Rolle’s Theorem is not applicable for the function f in interval [1, 3].

(v) f (x) = x^2/3 on [-1, 1]

Solution:

Solution:

2. Verify the Rolle’s Theorem for each of the following functions on the indicated intervals:

(i) f (x) = x² – 8x + 12 on [2, 6]

Solution:

(ii) f(x) = x² – 4x + 3 on [1, 3]

Solution:

(iii) f (x) = (x – 1) (x – 2)² on [1, 2]

Solution:

Mean Value Theorems Ex 15.1 Q2(iv)

Mean Value Theorems Ex 15.1 Q2(v)

Mean Value Theorems Ex 15.1 Q2(vi)

Mean Value Theorems Ex 15.1 Q2(vii)

Mean Value Theorems Ex 15.1 Q2(viii)

Mean Value Theorems Ex 15.1 Q3(i)

Mean Value Theorems Ex 15.1 Q3(ii)

Mean Value Theorems Ex 15.1 Q3(iii)

Mean Value Theorems Ex 15.1 Q3(iv)

Mean Value Theorems Ex 15.1 Q3(v)

Mean Value Theorems Ex 15.1 Q3(vi)

Mean Value Theorems Ex 15.1 Q3(vii)

Mean Value Theorems Ex 15.1 Q3(viii)

Mean Value Theorems Ex 15.1 Q3(ix)

Mean Value Theorems Ex 15.1 Q3(x)

Mean Value Theorems Ex 15.1 Q3(xi)

Mean Value Theorems Ex 15.1 Q3(xii)

Mean Value Theorems Ex 15.1 Q3(xiii)

Mean Value Theorems Ex 15.1 Q3(xiv)


Mean Value Theorems Ex 15.1 Q3(xv)

Mean Value Theorems Ex 15.1 Q3(xvi)

Mean Value Theorems Ex 15.1 Q3(xvii)

Mean Value Theorems Ex 15.1 Q3(xvii)

Mean Value Theorems Ex 15.1 Q3(xviii)

Mean Value Theorems Ex 15.1 Q7

Mean Value Theorems Ex 15.1 Q8(i)

Mean Value Theorems Ex 15.1 Q8(ii)

Mean Value Theorems Ex 15.1 Q8(iii)

Mean Value Theorems Ex 15.1 Q9

Mean Value Theorems Ex 15.1 Q10




Mean Value Theorems Ex 15.1 Q11

RD Sharma Class 12 Solutions Chapter 15 Exercise 15.1 | Important Concepts

The following are some of the most essential topics of this exercise.

• Rolle’s theorem
• Geometrical interpretation of Rolle’s theorem
• Algebraic interpretation of Rolle’s theorem
• Checking the applicability of Rolle’s theorem
• Verification of Rolle’s theorem for a given function defined on a given interval
• Miscellaneous applications of Rolle’s theorem

RD Sharma Solutions for Class 12 Maths Chapter 15 Exercise 15.1 are immensely helpful while doing your homework and also while preparing for CBSE finals. If you have any queries, feel free to ask us in the comment section below.

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