Applications of Derivatives Test

Result

Applications of Derivatives Test - 2

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

If the function f (x) = 2x³ − 9ax² + 12a² x + 1, where a > 0, attains its maximum and minimum at p and q respectively such that p² = q, then a equals

A
3

B
1

C
2

D
1/2

Solution

Clearly f″ (x) > 0 for x = 2a ⇒ q = 2a < 0 for x = a ⇒ p = a
or p² = q ⇒ a = 2.
Hence, (C) is the correct answer.
Question 2
1 / -0

The real number k for which the equation, 2x³ + 3x + k = 0 has two distinct real roots in [0, 1]

A
lies between 2 and 3

B
lies between −1 and 0

C
does not exist

D
lies between 1 and 2

Solution

If 2x³ + 3x + k = 0 has 2 distinct real roots in [0, 1], then f′ (x) will change sign
but f′(x) = 6x² + 3 > 0
So no value of k exists.
Hence option C is correct.