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Maths Application of Derivatives Class 12 Assertion and Reason Questions

Assertion Reasoning Quiz · Class 12 · Maths · CBSE

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Chapter 6 Class 12 Application of Derivatives | 5 questions | about 4 minutes

Practise Application of Derivatives Class 12 with Teachoo's Assertion Reasoning Quiz (Class 12 · Maths · CBSE). Practise these questions in a free interactive quiz with answer feedback.

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Question 1 of 5
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Question 1 of 5
Assertion (A): The function \(f(x)=x+\frac{1}{x}\) has a local minimum at \(x=1\).
Reason \((\mathrm{R})\) : \(f^{\prime}(1)=0\) and \(f^{\prime \prime}(1)>0\).
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Question 2 of 5
Assertion (A): The function \(f(x)=e^x\) has no local maximum or minimum.
Reason (R): The derivative of the function, \(f^{\prime}(x)=e^x\), is never equal to zero.
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Question 3 of 5
Assertion (A): The function \(f(x)=\sin (x)\) is increasing on the interval \(\left(0, \frac{\pi}{2}\right)\).
Reason (R): The derivative, \(f^{\prime}(x)=\cos (x)\), is positive for all \(x\) in the interval ( \(0, \frac{\pi}{2}\))
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Question 4 of 5
Assertion (A): The function \(f(x)=x^2\) is decreasing on the interval \((-\infty, 0)\).
Reason (R): The derivative \(f^{\prime}(x)=2 x\) is negative for all \(x\) in the interval ( \(-\infty, 0\)).
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Question 5 of 5
Assertion (A): A point \(c\) where \(f^{\prime}(c)=0\) must be a point of local extremum.
Reason (R): The tangent to the curve at \(x=c\) is horizontal.
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