Teachoo MCQ Test

Assertion Reasoning Quiz

Chapter 6 Class 12 Application of Derivatives | 5 questions

Timed test. Answer every question before time runs out. Correct answers and solutions appear after submission.
Time remaining 360
Question 1 of 5
Question 1 of 5
Assertion (A): The absolute maximum of \(f(x)=x^2\) on the interval \([-2,2]\) is 4 .
Reason (R): The absolute maximum of a function on a closed interval must occur at a critical point or an endpoint.
Select one option. Answers are shown after the test.
Question 2 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 ( \(-\infty, 0\)).
Select one option. Answers are shown after the test.
Question 3 of 5
Assertion (A): If the marginal revenue of a company is greater than its marginal cost, it should increase production.
Reason (R): The rate of change of profit is positive when MR \(>\mathrm{MC}\).
Select one option. Answers are shown after the test.
Question 4 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.
Select one option. Answers are shown after the test.
Question 5 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 ( \(0, \frac{\pi}{2}\))
Select one option. Answers are shown after the test.