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Maths Application of Derivatives Class 12 MCQ Questions

Question 1 of 10
Question 1 of 10
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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Question 2 of 10
Assertion (A): A cylindrical can of a given volume has minimum surface area when its height is equal to its diameter.
Reason (R): The second derivative of the surface area function with respect to the radius is positive at the critical point.
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Question 3 of 10
NCERT Exemplar
The function \(f(x)=x^{\wedge} 3\) has \(f^{\prime}(0)=0\). What is true about the point \(x=0\) ?
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Question 4 of 10
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A function \(f(x)\) is increasing on the interval ( \(a, b\) ). What can be said about its derivative, \(f^{\prime}(x)\) ?
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Question 5 of 10
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Water is draining from a conical tank. The rate at which the water level \(h\) is dropping is related to the radius \(r\) of the water's surface. This is a classic example of
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Question 6 of 10
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A critical point of a function \(f\) is a point \(c\) where:
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Question 7 of 10
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The interval on which the function \(f(x)=2 x^3+9 x^2+12 x-1\) is decreasing is:
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Question 8 of 10
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A company's marginal cost is the derivative of its cost function, \(C^{\prime}(x)\). If \(C^{\prime}(100)=\) 15, what does this signify?
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Question 9 of 10
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Maximum slope of the curve \(y=-x^3+3 x^2+9 x-27\) is:
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Question 10 of 10
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The slope of the tangent line to the curve \(y=\mathrm{x}^2-3 x\) at \(x=1\) represents:
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10 Question MCQ (including Assertion) · Class 12 · Maths · CBSE

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Chapter 6 Class 12 Application of Derivatives | 10 questions | about 8 minutes

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