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BCA Semester 2 – Mathematics II – Unit 3: Application of Differentiation (8Hrs)

Comprehensive questions and detailed answers for Unit 3: Application of Differentiation (8Hrs). Perfect for exam preparation and concept clarity.

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State Rolle's Theorem. Verify Rolle's Theorem for the function

f(x)=x^2-9

in the interval $-3 \le x \le 3$ .

MediumNumerical5 marks2022(TU FOHSS Final)

What do you mean by stationary points and inflection points?
Using derivatives, find two numbers whose sum is 20 and the sum of whose squares is minimum.

HardNumerical10 marks2022(TU FOHSS Final)

Verify Rolle's theorem for the function $f(x) = \sin x,\quad x \in [0,\pi]$ and find the point on the curve where the tangent is parallel to the $x$ -axis.

MediumNumerical5 marks2023(TU FOHSS Final)

Find the maximum and minimum values of the function

\quad \quad f(x) = x^3 + 6x^2 + 9x - 2

Also, find the point of inflection, if any.

MediumNumerical5 marks2023(TU FOHSS Final)

a. Verify $\text{Lagrange’s Mean Value Theorem}$ for the function

\quad \quad f(x) = \sqrt{x - 1},\quad x \in [1,3]

b. Solve the differential equation

\quad \quad xy \frac{dy}{dx} = x^2 + y^2

HardNumerical10 marks2023(TU FOHSS Final)

a) Using Simpson’s $\tfrac{1}{3}$ Rule, evaluate

\int_0^1 \frac{1}{1+2x^2}\,dx;\quad h = 0.25

b) Find the maximum and minimum values of the function

f(x) = 4x^3 - 15x^2 + 12x - 1

Also, find the point of inflection.

HardNumerical10 marks2024(TU FOHSS Final)

State Mean Value Theorem. Give its geometrical meaning.
Verify the Mean Value Theorem for the function

f(x) = x^3 + x^2 - 6x

in the interval $[-1,4]$ .

MediumTHEORY5 marks2024(TU FOHSS Final)

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Sample Questions

State Rolle's Theorem. Verify Rolle's Theorem for the function \[ f(x)=x^2-9 \] in the interval $ -3 \le x \le 3 $.

Marks: 5Chapter: Unit 3: Application of Differentiation (8Hrs)

What do you mean by stationary points and inflection points? Using derivatives, find two numbers whose sum is 20 and the sum of whose squares is minimum.

Marks: 10Chapter: Unit 3: Application of Differentiation (8Hrs)

Verify Rolle's theorem for the function $ f(x) = \sin x,\quad x \in [0,\pi] $ and find the point on the curve where the tangent is parallel to the $x$-axis.

Marks: 5Chapter: Unit 3: Application of Differentiation (8Hrs)

Find the maximum and minimum values of the function \[ \quad \quad f(x) = x^3 + 6x^2 + 9x - 2 \] Also, find the point of inflection, if any.

Marks: 5Chapter: Unit 3: Application of Differentiation (8Hrs)

a. Verify $$\text{Lagrange’s Mean Value Theorem}$$ for the function \[ \quad \quad f(x) = \sqrt{x - 1},\quad x \in [1,3] \] b. Solve the differential equation \[ \quad \quad xy \frac{dy}{dx} =

Marks: 10Chapter: Unit 3: Application of Differentiation (8Hrs)

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BCA Semester 2 – Mathematics II – Unit 3: Application of Differentiation (8Hrs)

Sample Questions

State Rolle's Theorem. Verify Rolle's Theorem for the function \[ f(x)=x^2-9 \] in the interval \( -3 \le x \le 3 \).

What do you mean by stationary points and inflection points? Using derivatives, find two numbers whose sum is 20 and the sum of whose squares is minimum.

Verify Rolle's theorem for the function \( f(x) = \sin x,\quad x \in [0,\pi] \) and find the point on the curve where the tangent is parallel to the \(x\)-axis.

Find the maximum and minimum values of the function \[ \quad \quad f(x) = x^3 + 6x^2 + 9x - 2 \] Also, find the point of inflection, if any.

a. Verify $$\text{Lagrange’s Mean Value Theorem}$$ for the function \[ \quad \quad f(x) = \sqrt{x - 1},\quad x \in [1,3] \] b. Solve the differential equation \[ \quad \quad xy \frac{dy}{dx} =