SATHEE: Limit Continuity and Differentiability 7 Question 4

Limit Continuity and Differentiability 7 Question 4

4. Let $S$ be the set of all points in $(- π, π)$ at which the function, $f (x) = min \sin x, \cos x$ is not differentiable. Then, $S$ is a subset of which of the following?

(a) $- \frac{π}{4}, 0, \frac{π}{4}$

(b) $- \frac{π}{2}, - \frac{π}{4}, \frac{π}{4}, \frac{π}{2}$

(d) $- \frac{3 π}{4}, - \frac{π}{2}, \frac{π}{2}, \frac{3 π}{4}$

(2019 Main, 12 Jan I)

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Answer:

Correct Answer: 4. (c)

Solution:

Let $y = f (f (f (x))) + (f (x))^{2}$

On differentiating both sides w.r.t. $x$ , we get

$\frac{d y}{d x} = f^{'} (f (f (x))) \cdot f^{'} (f (x)) \cdot f^{'} (x) + 2 f (x) f^{'} (x)$

[by chain rule]

$\begin{aligned} So, {\frac{d y}{d x} |}_{at x = 1} = f^{'} (f (f (1))) \cdot f^{'} (f (1)) \cdot f^{'} (1) + 2 f (1) f^{'} (1) \\ {∴ \frac{d y}{d x} |}_{x = 1} = f^{'} (f (1)) \cdot f^{'} (1) \cdot (3) + 2 (1) (3) \\ = f^{'} (1) \cdot (3) \cdot (3) + 6 \\ = (3 \times 9) + 6 = 27 + 6 = 33 \end{aligned}$

Limit Continuity and Differentiability 7 Question 4

4. Let $S$ be the set of all points in $(- π, π)$ at which the function, $f (x) = min \sin x, \cos x$ is not differentiable. Then, $S$ is a subset of which of the following?

Answer:

Engineering Preparation

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NCERT Books & Solutions

Important Resources

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Syllabus

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Sample Mock Test

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NCERT Exercise Video Solution

Limit Continuity and Differentiability 7 Question 4

4. Let S be the set of all points in (−π,π) at which the function, f(x)=minsin⁡x,cos⁡x is not differentiable. Then, S is a subset of which of the following?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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4. Let $S$ be the set of all points in $(- π, π)$ at which the function, $f (x) = min \sin x, \cos x$ is not differentiable. Then, $S$ is a subset of which of the following?